Introduction To Metric And Topological Spaces

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Introduction to Metric and Topological Spaces

Author : Wilson A Sutherland
Publisher : Oxford University Press
ISBN 13 : 0191568309
Total Pages : 219 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Introduction to Metric and Topological Spaces by : Wilson A Sutherland

Download or read book Introduction to Metric and Topological Spaces written by Wilson A Sutherland and published by Oxford University Press. This book was released on 2009-06-18 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 new edition of Wilson Sutherland's classic text 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, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.

Introduction to Metric and Topological Spaces

Author : Wilson A Sutherland
Publisher : Oxford University Press
ISBN 13 : 0199563071
Total Pages : 219 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Introduction to Metric and Topological Spaces by : Wilson A Sutherland

Introduction to Metric and Topological Spaces

Author : Wilson Alexander Sutherland
Publisher :
ISBN 13 : 9781383046182
Total Pages : 0 pages
Book Rating : 4.0/5 (461 download)

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Book Synopsis Introduction to Metric and Topological Spaces by : Wilson Alexander Sutherland

Download or read book Introduction to Metric and Topological Spaces written by Wilson Alexander Sutherland and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.

Introduction to Metric and Topological Spaces

Author : Wilson Alexander Sutherland
Publisher : Oxford University Press
ISBN 13 : 9780198531616
Total Pages : 200 pages
Book Rating : 4.5/5 (316 download)

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Book Synopsis Introduction to Metric and Topological Spaces by : Wilson Alexander Sutherland

Download or read book Introduction to Metric and Topological Spaces written by Wilson Alexander Sutherland and published by Oxford University Press. This book was released on 1975 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topology of Metric Spaces

Author : S. Kumaresan
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9781842652503
Total Pages : 172 pages
Book Rating : 4.6/5 (525 download)

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Book Synopsis Topology of Metric Spaces by : S. Kumaresan

Download or read book Topology of Metric Spaces written by S. Kumaresan and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.

Introduction to Topology

Author : Theodore W. Gamelin
Publisher : Courier Corporation
ISBN 13 : 0486320189
Total Pages : 258 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Introduction to Topology by : Theodore W. Gamelin

Download or read book Introduction to Topology written by Theodore W. Gamelin and published by Courier Corporation. This book was released on 2013-04-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

An Introduction to Metric Spaces and Fixed Point Theory

Author : Mohamed A. Khamsi
Publisher : John Wiley & Sons
ISBN 13 : 1118031326
Total Pages : 318 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis An Introduction to Metric Spaces and Fixed Point Theory by : Mohamed A. Khamsi

Download or read book An Introduction to Metric Spaces and Fixed Point Theory written by Mohamed A. Khamsi and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diese Einfuhrung in das Gebiet der metrischen Raume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausfuhrlich und anschaulich werden die Grundlagen von metrischen Raumen und Banach-Raumen erklart, Anhange enthalten Informationen zu verschiedenen Schlusselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschaftigen sich mit fortgeschritteneren Themen.

Set Theory and Metric Spaces

Author : Irving Kaplansky
Publisher : American Mathematical Society
ISBN 13 : 1470463849
Total Pages : 140 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Set Theory and Metric Spaces by : Irving Kaplansky

Download or read book Set Theory and Metric Spaces written by Irving Kaplansky and published by American Mathematical Society. This book was released on 2020-09-10 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book that could profitably be read by many graduate students or by seniors in strong major programs … has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. … There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem … The presentation of metric spaces before topological spaces … should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. —Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. — Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.

Real Variables with Basic Metric Space Topology

Author : Robert B. Ash
Publisher : Courier Corporation
ISBN 13 : 0486151492
Total Pages : 216 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Real Variables with Basic Metric Space Topology by : Robert B. Ash

Download or read book Real Variables with Basic Metric Space Topology written by Robert B. Ash and published by Courier Corporation. This book was released on 2014-07-28 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.

Topological Spaces

Author : Gerard Buskes
Publisher : Springer Science & Business Media
ISBN 13 : 1461206650
Total Pages : 321 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Topological Spaces by : Gerard Buskes

Download or read book Topological Spaces written by Gerard Buskes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Topology

Author : Bert Mendelson
Publisher : Courier Corporation
ISBN 13 : 0486135098
Total Pages : 226 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Topology by : Bert Mendelson

Download or read book Introduction to Topology written by Bert Mendelson and published by Courier Corporation. This book was released on 2012-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Introduction to Set Theory and Topology

Author : Kazimierz Kuratowski
Publisher : Elsevier
ISBN 13 : 1483151638
Total Pages : 352 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Introduction to Set Theory and Topology by : Kazimierz Kuratowski

Download or read book Introduction to Set Theory and Topology written by Kazimierz Kuratowski and published by Elsevier. This book was released on 2014-07-10 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

A Course in Metric Geometry

Author : Dmitri Burago
Publisher : American Mathematical Society
ISBN 13 : 1470468530
Total Pages : 415 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Course in Metric Geometry by : Dmitri Burago

Download or read book A Course in Metric Geometry written by Dmitri Burago and published by American Mathematical Society. This book was released on 2022-01-27 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.

Topology with Applications

Author : Somashekhar A. Naimpally
Publisher : World Scientific
ISBN 13 : 9814407666
Total Pages : 294 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology with Applications by : Somashekhar A. Naimpally

Download or read book Topology with Applications written by Somashekhar A. Naimpally and published by World Scientific. This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Point Set Topology

Author : John D. Baum
Publisher : Courier Corporation
ISBN 13 : 0486668266
Total Pages : 164 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Elements of Point Set Topology by : John D. Baum

Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Introduction to Topological Manifolds

Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 038722727X
Total Pages : 395 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Topological Manifolds by : John M. Lee

Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Topology

Author : Stefan Waldmann
Publisher : Springer
ISBN 13 : 331909680X
Total Pages : 136 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Topology by : Stefan Waldmann

Download or read book Topology written by Stefan Waldmann and published by Springer. This book was released on 2014-08-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.