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Format: 1 online resource (xiii, 271 pages) : , illustrations.

Edition: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011.

ISBN: 9781118031582 , 111803158X , 9781118030585 , 1118030583

Series Statement: Pure and applied mathematics

Content: This text covers the essentials of point-set topology in a relatively terse presentation, with lots of examples and motivation along the way. Along with the standard point-set topology topics (connected spaces, compact spaces, separation axioms, and metric spaces), the author includes path-connectedness, and a chapter on constructing spaces from other spaces (including products, quotients, etc.). The text culminates in to two main chapters, each independent of the other: 1) The Classification Theorem for Compact, Connected Surfaces and 2) Fundamental Groups and Covering Spaces, with Applications giving the reader the choice of which subject best suits them.

Note: Front Matter -- Introduction: Intuitive Topology -- Background on Sets and Functions -- Topological Spaces -- More on Open and Closed Sets and Continuous Functions -- New Spaces from Old -- Connected Spaces -- Compact Spaces -- Separation Axioms -- Metric Spaces -- The Classification of Surfaces -- Fundamental Groups and Covering Spaces -- References -- Index -- Pure and Applied Mathematics. , foreword -- , Acknowledgments -- , Introduction : Intuitive topology -- , Introduction : intuitive topology -- , Background on sets and functions -- , Sets -- , Functions -- , Equivalence relations -- , Induction -- , Cardinal numbers -- , Groups -- , Topological spaces -- , Introduction -- , Definitions and examples -- , Basics on open and closed sets -- , The subspace topology -- , Continuous functions -- , More on open and closed sets and continuous functions -- , Introduction -- , Basis for a topology -- , Limit points -- , Interior, boundary and closure -- , More on continuity -- , New spaces from old -- , Introduction -- , Product spaces -- , Infinite product spaces (optional) -- , Quotient spaces -- , Unions and wedges -- , Connected spaces -- , Introduction -- , Definition, examples and properties -- , Connectedness in the real line -- , Path-connectedness -- , Connectedness of unions and finite products -- , Connnectedness of infinite products (optional) -- , Compact spaces -- , Introduction -- , Definition, examples and properties -- , Hausdorff spaces and compactness -- , Compactness in the real line -- , Compactness of products -- , Finite intersection property (optional). , Separation axioms -- , Introduction -- , Definition and examples -- , Regular and normal spaces -- , Separation axioms and compactness -- , Metric spaces -- , Introduction -- , Definition and examples -- , Properties of metric spaces -- , Basics on sequences -- , The classification of surfaces -- , Introduction -- , Surfaces and higher-dimensional manifolds -- , Connected sums of surfaces -- , The classification theorem -- , Triangulations of surfaces -- , Proof of the classification theorem -- , Euler characteristics and uniqueness -- , Fundamental groups and covering spaces -- , Introduction -- , Homotopy of functions and paths -- , An operation on paths -- , The fundamental group -- , Covering spaces -- , Fundamental group of the circle and related spaces -- , The fundamental groups of surfaces -- , References -- , Index. , Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

Additional Edition: Print version: Shick, Paul Louis, 1956- Topology. Hoboken, N.J. : Wiley-Interscience, ©2007 ISBN 0470096055

Language: English

Subjects: Mathematics

Keywords: Electronic books. ; Einführung.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118031582