UID:
almahu_9948197630602882
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