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  • Introduction to Topology: Third Edition by Bert Mendelson (English) Paperback Bo

    • Item No : 156883246120
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      Introduction to Topology

      by Bert Mendelson

      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.

      FORMAT
      Paperback
      LANGUAGE
      English
      CONDITION
      Brand New


      Publisher Description

      Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.

      Back Cover

      Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure. The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n -space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented. Unabridged Dover (1990) republication of the edition published by Allyn and Bacon, Inc., Boston 1975.

      Table of Contents

      Preface 1 Theory of Sets 1 Introduction 2 Sets and subsets 3 "Set operations: union, intersection, and complement" 4 Indexed families of sets 5 Products of sets 6 Functions 7 Relations 8 Composition of functions and diagrams 9 "Inverse functions, extensions, and restrictions" 10 Arbitrary products 2 Metric Spaces 1 Introduction 2 Metric spaces 3 Continuity 4 Open balls and neighborhoods 5 Limits 6 Open sets and closed sets 7 Subspaces and equivalence of metric spaces 8 An infinite dimensional Euclidean space 3 Topological Spaces 1 Introduction 2 Topological spaces 3 Neighborhoods and neighborhood spaces 4 "Closure, interior, boundary" 5 "Functions, continuity, homeomorphism" 6 Subspaces 7 Products 8 Identification topologies 9 Categories and functors 4 Connectedness 1 Introduction 2 Connectedness 3 Connectedness on the real line 4 Some applications of connectedness 5 Components and local connectedness 6 Path-connected topological spaces 7 Homotopic paths and the fundamental group 8 Simple connectedness 5 Compactness 1 Introduction 2 Compact topological spaces 3 Compact subsets of the real line 4 Products of compact spaces 5 Compact metric spaces 6 Compactness and the Bolzano-Weierstrass property 7 Surfaces by identification Bibliography Index

      Long Description

      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.

      Details

      ISBN0486663523
      Author Bert Mendelson
      Pages 224
      Language English
      Edition 3rd
      ISBN-10 0486663523
      ISBN-13 9780486663524
      Media Book
      Format Paperback
      DEWEY 514
      Imprint Dover Publications Inc.
      Place of Publication New York
      Country of Publication United States
      Illustrations 51ill.
      Short Title INTRO TO TOPOLOGY 3/E
      Birth 1926
      Subtitle Third Edition
      DOI 10.1604/9780486663524
      AU Release Date 2003-03-17
      NZ Release Date 2003-03-17
      UK Release Date 2003-03-28
      Publisher Dover Publications Inc.
      Edition Description 3rd Revised edition
      Year 2003
      Publication Date 2003-03-28
      Audience Undergraduate
      US Release Date 2003-03-28
      Series Dover Books on Mathema 1.4tics

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