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Open Problems in Topology II

Open Problems in Topology II Book
Author : Elliott M. Pearl
Publisher : Elsevier
Release : 2011-08-11
ISBN : 9780080475295
Language : En, Es, Fr & De

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Book Description :

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world

Recent Progress in General Topology II

Recent Progress in General Topology II Book
Author : M. Husek,J. van Mill
Publisher : Elsevier
Release : 2002-11-13
ISBN : 0080929958
Language : En, Es, Fr & De

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Book Description :

The book presents surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as: R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.

Recent Progress in General Topology II

Recent Progress in General Topology II Book
Author : Miroslav Hušek,J. van Mill
Publisher : Elsevier
Release : 2002
ISBN : 0444509801
Language : En, Es, Fr & De

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Book Description :

The book presents surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as: R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.

Open Problems in Topology

Open Problems in Topology Book
Author : J. van Mill,George M. Reed,Elliot Pearl
Publisher : North Holland
Release : 1990
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

From the Introduction: This volume grew from a discussion by the editors on the difficulty of finding good thesis problems for graduate students in topology. Although at any given time we each had our own favorite problems, we acknowledged the need to offer students a wider selection from which to choose a topic peculiar to their interests. One of us remarked, 'Wouldn't it be nice to have a book of current unsolved problems always available to pull down from the shelf?' The other replied 'Why don't we simply produce such a book?' Two years later and not so simply, here is the resulting volume. The intent is to provide not only a source book for thesis-level problems but also a challenge to the best researchers in the field.

Recent Progress in General Topology III

Recent Progress in General Topology III Book
Author : K.P. Hart,J. van Mill,P. Simon
Publisher : Springer Science & Business Media
Release : 2013-12-11
ISBN : 946239024X
Language : En, Es, Fr & De

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Book Description :

The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Set Theory and Its Applications

Set Theory and Its Applications Book
Author : Liljana Babinkostova
Publisher : American Mathematical Soc.
Release : 2011
ISBN : 0821848127
Language : En, Es, Fr & De

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Book Description :

This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.

A Cp Theory Problem Book

A Cp Theory Problem Book Book
Author : Vladimir V. Tkachuk
Publisher : Springer
Release : 2016-04-05
ISBN : 3319243853
Language : En, Es, Fr & De

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Book Description :

This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.

Ischia Group Theory 2010

Ischia Group Theory 2010 Book
Author : Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj
Publisher : World Scientific
Release : 2012
ISBN : 9814350389
Language : En, Es, Fr & De

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Book Description :

The papers in this volume represent the proceedings of the Conference entitled "Ischia Group Theory 2010," which took place at NH Ischia Thermal SPA Resort, Ischia, Naples, Italy, from April 14 to April 17, 2010. The articles in this volume are contributions by speakers and participants of the Conference. The volume contains a collection of research articles by leading experts in group theory and some accessible surveys of recent research in the area. Together they provide an overview of the diversity of themes and applications that interest group theorists today. Topics covered in this volume include: finite p-groups, character and representation theory, combinatorial group theory, varieties of groups, profinite and pro-p-groups, linear groups, graphs connected with groups, subgroup structure, finiteness conditions, radical rings, conjugacy classes, automorphisms.

Monoidal Topology

Monoidal Topology Book
Author : Dirk Hofmann,Gavin J. Seal,Walter Tholen
Publisher : Cambridge University Press
Release : 2014-07-31
ISBN : 1139993283
Language : En, Es, Fr & De

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Book Description :

Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly extended from set maps to V-valued relations, the book develops a categorical theory of (T,V)-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book.

Recent Progress in General Topology II

Recent Progress in General Topology II  Book
Author : A. Arhangel'skii
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The book presents surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the previous edition (North Holland, 1992), ""Open Problems in Topology"" (North Holland, 1990) and ""Handbook of Set-Theoretic Topology"" (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The fol.

Basic Algebraic Topology and its Applications

Basic Algebraic Topology and its Applications Book
Author : Mahima Ranjan Adhikari
Publisher : Springer
Release : 2016-09-16
ISBN : 813222843X
Language : En, Es, Fr & De

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Book Description :

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Robust Chaos and Its Applications

Robust Chaos and Its Applications Book
Author : Elhadj Zeraoulia,Julien Clinton Sprott
Publisher : World Scientific
Release : 2011-10-17
ISBN : 9814458090
Language : En, Es, Fr & De

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Book Description :

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular. Contents: Poincaré Map Technique, Smale Horseshoe, and Symbolic DynamicsRobustness of ChaosStatistical Properties of Chaotic AttractorsStructural StabilityTransversality, Invariant Foliation, and the Shadowing LemmaChaotic Attractors with Hyperbolic StructureRobust Chaos in Hyperbolic SystemsLorenz-Type SystemsRobust Chaos in the Lorenz-Type SystemsNo Robust Chaos in Quasi-AttractorsRobust Chaos in One-Dimensional MapsRobust Chaos in 2-D Piecewise Smooth Maps Readership: Advanced undergraduate and graduate students, researchers, engineers and instructors interested in chaos and dynamical systems. Keywords:Poincaré;Map Technique;Smale Horseshoe;Symbolic Dynamics;Robustness of Chaos;Statistical Properties of Chaotic Attractors;Structural Stability Transversality;Invariant Foliation;Shadowing Lemma;Hyperbolic Structure;Lorenz-Type Systems;Quasi-Attractors;Robust Chaos in One Dimensional Maps;Robust Chaos in 2-D Piecewise Smooth Maps

Nonlinear Polymer Rheology

Nonlinear Polymer Rheology Book
Author : Shi-Qing Wang
Publisher : John Wiley & Sons
Release : 2018-01-02
ISBN : 111902904X
Language : En, Es, Fr & De

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Book Description :

Integrating latest research results and characterization techniques, this book helps readers understand and apply fundamental principles in nonlinear polymer rheology. The author connects the basic theoretical framework with practical polymer processing, which aids practicing scientists and engineers to go beyond the existing knowledge and explore new applications. Although it is not written as a textbook, the content can be used in an upper undergraduate and first year graduate course on polymer rheology. • Describes the emerging phenomena and associated conceptual understanding in the field of nonlinear polymer rheology • Incorporates details on latest experimental discoveries and provides new methodology for research in polymer rheology • Integrates latest research results and new characterization techniques like particle tracking velocimetric method • Focuses on the issues concerning the conceptual and phenomenological foundations for polymer rheology • Has a companion website for readers to access with videos complementing the content within several chapters

Bodies of Constant Width

Bodies of Constant Width Book
Author : Horst Martini,Luis Montejano,Déborah Oliveros
Publisher : Springer
Release : 2019-03-16
ISBN : 3030038688
Language : En, Es, Fr & De

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Book Description :

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.

History of Topology

History of Topology Book
Author : I.M. James
Publisher : Elsevier
Release : 1999-08-24
ISBN : 9780080534077
Language : En, Es, Fr & De

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Book Description :

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards. As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2008-10
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Descriptive Topology in Selected Topics of Functional Analysis

Descriptive Topology in Selected Topics of Functional Analysis Book
Author : Jerzy Kąkol,Wiesław Kubiś,Manuel López-Pellicer
Publisher : Springer Science & Business Media
Release : 2011-08-30
ISBN : 1461405297
Language : En, Es, Fr & De

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Book Description :

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.

Frontiers in the Study of Chaotic Dynamical Systems with Open Problems

Frontiers in the Study of Chaotic Dynamical Systems with Open Problems Book
Author : Elhadj Zeraoulia,Julien C. Sprott
Publisher : World Scientific
Release : 2011
ISBN : 9814340693
Language : En, Es, Fr & De

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Book Description :

This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.

Handbook of Geometry and Topology of Singularities II

Handbook of Geometry and Topology of Singularities II Book
Author : José Luis Cisneros-Molina
Publisher : Springer Nature
Release : 2021-12-07
ISBN : 3030780244
Language : En, Es, Fr & De

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Book Description :

Download Handbook of Geometry and Topology of Singularities II book written by José Luis Cisneros-Molina, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Open Problems in the Geometry and Analysis of Banach Spaces

Open Problems in the Geometry and Analysis of Banach Spaces Book
Author : Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer
Release : 2016-07-26
ISBN : 3319335723
Language : En, Es, Fr & De

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Book Description :

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.