General Topology

Author: George A. Duckett
Publisher: Createspace Independent Publishing Platform
ISBN: 1533137889
Release Date: 2016-05-08
Genre:

If you have a question about General Topology this is the book with the answers. General Topology: Questions and Answers takes some of the best questions and answers asked on the math.stackexchange.com website. You can use this book to look up commonly asked questions, browse questions on a particular topic, compare answers to common topics, check out the original source and much more. This book has been designed to be very easy to use, with many internal references set up that makes browsing in many different ways possible. Topics covered include: Real Analysis, Compactness, Metric Spaces, Algebraic Topology, Functional Analysis, Reference Request, Topological Groups, Manifolds, Connectedness, Analysis, Differential Geometry, Continuity, Set Theory, Category Theory and many more."

Counterexamples in Topology

Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 9780486319292
Release Date: 2013-04-22
Genre: Mathematics

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

Open Problems in Topology II

Author: Elliott M. Pearl
Publisher: Elsevier
ISBN: 0080475299
Release Date: 2011-08-11
Genre: Mathematics

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

Topics in General Topology

Author: K. Morita
Publisher: Elsevier
ISBN: 0080879888
Release Date: 1989-08-04
Genre: Mathematics

Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments. The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.

Introductory Topology

Author: Mohammed Hichem Mortad
Publisher: World Scientific Publishing Company
ISBN: 9789814583831
Release Date: 2014-02-28
Genre: Mathematics

The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.

Generalized Metric Spaces and Mappings

Author: Shou Lin
Publisher: Springer
ISBN: 9789462392168
Release Date: 2016-10-20
Genre: Mathematics

The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.

Recent Progress in General Topology III

Author: K.P. Hart
Publisher: Springer Science & Business Media
ISBN: 9789462390249
Release Date: 2013-12-11
Genre: Mathematics

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.

Surveys in General Topology

Author: George M. Reed
Publisher: Academic Press
ISBN: 9781483263861
Release Date: 2014-05-10
Genre: Mathematics

Surveys in General Topology presents topics relating to general topology ranging from closed mappings and ultrafilters to covering and separation properties of box products. Ordered topological spaces and the use of combinatorial techniques in functional analysis are also considered, along with product spaces and weakly compact subsets of Banach spaces. Applications of stationary sets in topology are presented as well. Comprised of 15 chapters, this volume begins with an analysis of some of the techniques and results in the area of closed mappings, followed by a discussion on the theory of ultrafilters. The reader is then introduced to the question of when a box product of compact spaces is paracompact, and how badly a box product of compact or metrizable spaces can fail to be normal. Subsequent chapters focus on the transfinite dimension; the properties of metacompactness, submetacompactness, and subparacompactness; the dimension of ordered topological spaces; the use of combinatorial techniques for the treatment and solution of fundamental problems in functional analysis, particularly in the isomorphic theory of Banach spaces; and order-theoretic base axioms. This monograph will be of significant value both to researchers in general topology and to mathematicians outside the field who wish an overview of current topics and techniques.

Elementary Topology

Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher: American Mathematical Soc.
ISBN: 0821886258
Release Date:
Genre:


Topological Methods in Group Theory

Author: Ross Geoghegan
Publisher: Springer Science & Business Media
ISBN: 9780387746111
Release Date: 2007-12-17
Genre: Mathematics

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Topology and Geometry for Physicists

Author: Charles Nash
Publisher: Courier Corporation
ISBN: 9780486318363
Release Date: 2013-08-16
Genre: Mathematics

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.