Foundations Of Topology
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Foundations Of Topology
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Author : C. Wayne Patty
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2009
Foundations Of Topology written by C. Wayne Patty and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
Topology is a branch of pure mathematics that deals with the abstract relationships found in geometry and analysis. Written with the mature student in mind, Foundations of Topology, Second Edition, provides a user-friendly, clear, and concise introduction to this fascinating area of mathematics. The author introduces topics that are well motivated with thorough proofs that make them easy to follow. Historical comments are dispersed throughout the text, and exercises, varying in degree of difficulty, are found at the end of each chapter. Foundations of Topology is an excellent text for teaching students how to develop the skill to write clear and precise proofs.
Convergence Foundations Of Topology
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Author : Szymon Dolecki
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-05-13
Convergence Foundations Of Topology written by Szymon Dolecki and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Mathematics categories.
This textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets. Convergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis. Convergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.
Foundations Of General Topology
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Author : William J. Pervin
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Foundations Of General Topology written by William J. Pervin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.
Foundations Of Topology 2 E
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Author : Patty
language : en
Publisher:
Release Date : 2010-01-01
Foundations Of Topology 2 E written by Patty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with categories.
Topology is a branch of pure mathematics that considers the abstract relationships found within geometry and analysis. Written with the mathematically mature student in mind, Foundations of Topology, Second Edition, provides a user-friendly, clear, and concise introduction to this fascinating area of mathematics. The author introduces topics that are well-motivated with thorough proofs, making them easy to follow. Historical comments are dispersed throughout the text, and exercises that vary in degree of difficulty are found at the end of each chapter. Foundations of Topology is an excellent text for teaching students how to develop the skills necessary for writing clear and precise proofs.
Foundations Of Topology
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Author : Gerhard Preuß
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Foundations Of Topology written by Gerhard Preuß and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-27 with Mathematics categories.
A new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this setting semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, e.g. simple convergence, continuous convergence and uniform convergence. Various interesting results are presented which cannot be obtained by using topological or uniform spaces in the usual context. The text is self-contained with the exception of the last chapter, where the intuitive concept of nearness is incorporated in Convenient Topology (there exist already excellent expositions on nearness spaces).
The Foundations Of Topological Graph Theory
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Author : C.Paul Bonnington
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Foundations Of Topological Graph Theory written by C.Paul Bonnington and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.
Foundations Of Algebraic Topology
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Author : Samuel Eilenberg
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Foundations Of Algebraic Topology written by Samuel Eilenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Convergence Foundations Of Topology
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Author : Szymon Dolecki
language : en
Publisher:
Release Date : 2016
Convergence Foundations Of Topology written by Szymon Dolecki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Topology Geometry And Gauge Fields
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Author : Gregory L. Naber
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-24
Topology Geometry And Gauge Fields written by Gregory L. Naber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-24 with Mathematics categories.
Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Foundations Of Combinatorial Topology
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Author : L. S. Pontryagin
language : en
Publisher: Courier Corporation
Release Date : 2015-05-20
Foundations Of Combinatorial Topology written by L. S. Pontryagin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-20 with Mathematics categories.
Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.