Topological Spaces
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Topological Spaces
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Author : Gerard Buskes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Spaces written by Gerard Buskes 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.
gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.
Topology With Applications
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Author : Somashekhar A. Naimpally
language : en
Publisher: World Scientific
Release Date : 2013
Topology With Applications written by Somashekhar A. Naimpally and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.
Introduction To Metric And Topological Spaces
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Author : Wilson Alexander Sutherland
language : en
Publisher: Oxford University Press
Release Date : 1975
Introduction To Metric And Topological Spaces written by Wilson Alexander Sutherland and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This book introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces. The book is aimed primarily at the second-year mathematics student, and numerous exercises are included.
Introduction To Metric And Topological Spaces
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Author : Wilson A Sutherland
language : en
Publisher: Oxford University Press
Release Date : 2009-06-18
Introduction To Metric And Topological Spaces written by Wilson A Sutherland and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-18 with Mathematics categories.
This fully updated new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.
Topological Spaces
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Author : H. J. Kowalsky
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Topological Spaces written by H. J. Kowalsky 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.
Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.
Topological Spaces
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Author : Claude Berge
language : en
Publisher:
Release Date : 1877
Topological Spaces written by Claude Berge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1877 with Functional analysis categories.
Linear Topological Spaces
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Author : John Leroy Kelley
language : en
Publisher: Springer
Release Date : 2013-12-17
Linear Topological Spaces written by John Leroy Kelley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Mathematics categories.
Topology And Linear Topological Spaces
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Author : Hidegorō Nakano
language : en
Publisher:
Release Date : 1951
Topology And Linear Topological Spaces written by Hidegorō Nakano and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Linear topological spaces categories.
Topological Vector Spaces I
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Author : Gottfried Köthe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Vector Spaces I written by Gottfried Köthe 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.
It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.
Pseudocompact Topological Spaces
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Author : Michael Hrušák
language : en
Publisher: Springer
Release Date : 2018-07-19
Pseudocompact Topological Spaces written by Michael Hrušák and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.
This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.