# Open Problems in Topology II

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## Open Problems in Topology II

Author | : Elliott M. Pearl |

Publsiher | : Elsevier |

Total Pages | : 776 |

Release | : 2011-08-11 |

ISBN 10 | : 9780080475295 |

ISBN 13 | : 0080475299 |

Language | : EN, FR, DE, ES & NL |

**Open Problems in Topology II Book Review:**

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

Author | : Miroslav Hušek,J. van Mill |

Publsiher | : Elsevier |

Total Pages | : 638 |

Release | : 2002 |

ISBN 10 | : 0444509801 |

ISBN 13 | : 9780444509802 |

Language | : EN, FR, DE, ES & NL |

**Recent Progress in General Topology II Book Review:**

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

Author | : J. van Mill,George M. Reed,Elliot Pearl |

Publsiher | : North Holland |

Total Pages | : 692 |

Release | : 1990 |

ISBN 10 | : |

ISBN 13 | : UOM:39015018940943 |

Language | : EN, FR, DE, ES & NL |

**Open Problems in Topology Book Review:**

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 II

Author | : M. Husek,J. van Mill |

Publsiher | : Elsevier |

Total Pages | : 652 |

Release | : 2002-11-13 |

ISBN 10 | : 0080929958 |

ISBN 13 | : 9780080929958 |

Language | : EN, FR, DE, ES & NL |

**Recent Progress in General Topology II Book Review:**

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 Mathematics

Author | : John Forbes Nash, Jr.,Michael Th. Rassias |

Publsiher | : Springer |

Total Pages | : 543 |

Release | : 2016-07-05 |

ISBN 10 | : 3319321625 |

ISBN 13 | : 9783319321622 |

Language | : EN, FR, DE, ES & NL |

**Open Problems in Mathematics Book Review:**

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

## Unsolved Problems in Geometry

Author | : Hallard T. Croft,Kenneth Falconer,Richard K. Guy |

Publsiher | : Springer Science & Business Media |

Total Pages | : 199 |

Release | : 2012-12-06 |

ISBN 10 | : 1461209633 |

ISBN 13 | : 9781461209638 |

Language | : EN, FR, DE, ES & NL |

**Unsolved Problems in Geometry Book Review:**

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.

## Ultrafilters and Topologies on Groups

Author | : Yevhen G. Zelenyuk |

Publsiher | : Walter de Gruyter |

Total Pages | : 219 |

Release | : 2011 |

ISBN 10 | : 3110204223 |

ISBN 13 | : 9783110204223 |

Language | : EN, FR, DE, ES & NL |

**Ultrafilters and Topologies on Groups Book Review:**

This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results aboutultrafilters. Topics covered include: topological and left topological groups, ultrafilter semigroups, local homomorphisms and automorphisms, subgroups and ideal structure of ssG, almost maximal spaces and projectives of finite semigroups, resolvability of groups. This is a self-contained book aimed at graduate students and researchers working in topological algebra and adjacent areas. From the contents: Topological Groups Ultrafilters Topological Spaces with Extremal Properties Left Invariant Topologies and Strongly Discrete Filters Topological Groups with Extremal Properties The Semigroup ssS Ultrafilter Semigroups Finite Groups in ssG Ideal Structure of ssS Almost Maximal Topological Groups and Spaces Resolvability Open Problems "

## Elementary Topology

Author | : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 329 |

Release | : 2021 |

ISBN 10 | : 9780821886250 |

ISBN 13 | : 0821886258 |

Language | : EN, FR, DE, ES & NL |

**Elementary Topology Book Review:**

This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the proofs at the end of the chapter or skip them altogether. This style also caters to the expert who needs a handbook and prefers formulations not overshadowed by proofs. Most of the proofs are simple and easy to discover. The book can be useful and enjoyable for readers with quite different backgrounds and interests. The text is structured in such a way that it is easy to determine what to expect from each piece and how to use it. There is core material, which makes up a relatively small part of the book. The core material is interspersed with examples, illustrative and training problems, and relevant discussions. The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathematics. With almost no prerequisites (except real numbers), the book can serve as a text for a course on general and beginning algebraic topology.

## Lectures on the Topology of 3 Manifolds

Author | : Nikolai Saveliev |

Publsiher | : Walter de Gruyter |

Total Pages | : 199 |

Release | : 1999-01-01 |

ISBN 10 | : 3110806355 |

ISBN 13 | : 9783110806359 |

Language | : EN, FR, DE, ES & NL |

**Lectures on the Topology of 3 Manifolds Book Review:**

## Mathematical Reviews

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2008-10 |

ISBN 10 | : |

ISBN 13 | : UOM:39015082440762 |

Language | : EN, FR, DE, ES & NL |

**Mathematical Reviews Book Review:**

## Handbook of Set Theoretic Topology

Author | : K. Kunen,J. Vaughan |

Publsiher | : Elsevier |

Total Pages | : 1282 |

Release | : 2014-06-28 |

ISBN 10 | : 148329515X |

ISBN 13 | : 9781483295152 |

Language | : EN, FR, DE, ES & NL |

**Handbook of Set Theoretic Topology Book Review:**

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

## Topological Groups

Author | : Sidney A. Morris |

Publsiher | : MDPI |

Total Pages | : 160 |

Release | : 2019-03-05 |

ISBN 10 | : 303897644X |

ISBN 13 | : 9783038976448 |

Language | : EN, FR, DE, ES & NL |

**Topological Groups Book Review:**

Following the tremendous reception of our first volume on topological groups called "Topological Groups: Yesterday, Today, and Tomorrow", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

## The Scottish Book

Author | : R. Daniel Mauldin |

Publsiher | : Birkhäuser |

Total Pages | : 322 |

Release | : 2015-11-26 |

ISBN 10 | : 3319228978 |

ISBN 13 | : 9783319228976 |

Language | : EN, FR, DE, ES & NL |

**The Scottish Book Book Review:**

The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such areas as functional and real analysis, group theory, measure and set theory, probability, and topology. Finding solutions to the problems they proposed has been ongoing since World War II, with prizes offered in many cases to those who are successful. In the 35 years since the first edition published, several more problems have been fully or partially solved, but even today many still remain unsolved and several prizes remain unclaimed. In view of this, the editor has gathered new and updated commentaries on the original 193 problems. Some problems are solved for the first time in this edition. Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac, Antoni Zygmund, Paul Erdös, and Andrzej Granas that provide amazing insights into the mathematical environment of Lwów before World War II and the development of The Scottish Book. Also new in this edition are a brief history of the University of Wrocław’s New Scottish Book, created to revive the tradition of the original, and some selected problems from it. The Scottish Book offers a unique opportunity to communicate with the people and ideas of a time and place that had an enormous influence on the development of mathematics and try their hand on the unsolved problems. Anyone in the general mathematical community with an interest in the history of modern mathematics will find this to be an insightful and fascinating read.

## An Invitation to Knot Theory

Author | : Heather A. Dye |

Publsiher | : CRC Press |

Total Pages | : 256 |

Release | : 2018-09-03 |

ISBN 10 | : 1315362384 |

ISBN 13 | : 9781315362380 |

Language | : EN, FR, DE, ES & NL |

**An Invitation to Knot Theory Book Review:**

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.

## Topology

Author | : Tai-Danae Bradley,Tyler Bryson,John Terilla |

Publsiher | : Unknown |

Total Pages | : 168 |

Release | : 2020 |

ISBN 10 | : 0262539357 |

ISBN 13 | : 9780262539357 |

Language | : EN, FR, DE, ES & NL |

**Topology Book Review:**

"This book presents a modern, category-theory-based approach to topology to supplement the more traditional algebraic topology graduate course"--

## A Cp Theory Problem Book

Author | : Vladimir V. Tkachuk |

Publsiher | : Springer Science & Business Media |

Total Pages | : 488 |

Release | : 2011-03-23 |

ISBN 10 | : 9781441974426 |

ISBN 13 | : 1441974423 |

Language | : EN, FR, DE, ES & NL |

**A Cp Theory Problem Book Book Review:**

The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include: - A unique problem-based introduction to the theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.

## Old and New Unsolved Problems in Plane Geometry and Number Theory

Author | : Victor Klee,Stan Wagon |

Publsiher | : American Mathematical Soc. |

Total Pages | : 333 |

Release | : 2020-07-31 |

ISBN 10 | : 1470454610 |

ISBN 13 | : 9781470454616 |

Language | : EN, FR, DE, ES & NL |

**Old and New Unsolved Problems in Plane Geometry and Number Theory Book Review:**

Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.

## Unsolved Problems and Its Progress in General geometric Topology

Author | : Masami Sakai |

Publsiher | : Unknown |

Total Pages | : 86 |

Release | : 1999 |

ISBN 10 | : |

ISBN 13 | : OCLC:247737642 |

Language | : EN, FR, DE, ES & NL |

**Unsolved Problems and Its Progress in General geometric Topology Book Review:**

## Research Problems in Discrete Geometry

Author | : Peter Brass,William O. J. Moser,János Pach |

Publsiher | : Springer Science & Business Media |

Total Pages | : 500 |

Release | : 2006-06-19 |

ISBN 10 | : 0387238158 |

ISBN 13 | : 9780387238159 |

Language | : EN, FR, DE, ES & NL |

**Research Problems in Discrete Geometry Book Review:**

This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

## Questions and Answers in General Topology

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2003 |

ISBN 10 | : |

ISBN 13 | : CORNELL:31924099659751 |

Language | : EN, FR, DE, ES & NL |

**Questions and Answers in General Topology Book Review:**