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Introduction To Topology 3RD Editionby Bert Mendelson
Synopses & ReviewsPublisher Comments: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. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition. Synopsis: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. Synopsis:An undergraduate introduction to the fundamentals of topology — engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject. Description:Includes bibliographical references (p. 201202) and index.
Table of ContentsPreface
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 Pathconnected 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 BolzanoWeierstrass property 7 Surfaces by identification Bibliography Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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