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Basic topology

Author: M A Armstrong
Publisher: New York : Springer-Verlag, 1997, ©1983.
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : English : Corr. 5th printView all editions and formats
Summary:

In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating.

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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: M A Armstrong
ISBN: 0387908390 9780387908397 3540908390 9783540908395
OCLC Number: 38931320
Description: xii, 251 pages : illustrations ; 25 cm.
Contents: Introduction: --
Euler's theorem --
Topological equivalence --
Surfaces --
Abstract spaces --
A classification theorem --
Topological invariants --
Continuity: --
Open and close sets --
Continuous funtions --
A space-filling curve --
The Tietze extension theorem --
Compactness and connectedness: --
Closed bounded subsets of E" --
The Heine-Borel theorem --
Properties of compact spaces --
Product spaces --
Connectedness --
Joining points by paths --
Identification spaces: --
Constructing a Mobius strip --
The identification topology --
Topological groups --
Orbits spaces --
The fundamental group: --
Homotopic maps --
Construction of the fundamental group --
Calculations --
Homotopy type --
The Brouwer fixed-point of the plane --
Triangulations: --
Triangulating spaces --
Barycentric subdivision --
Simplicial approximation --
The edge group of a complex --
Triangulating orbit spaces --
Infinite complexes --
Surfaces: --
Classification --
Triangulation and orientation --
Euler characteristics --
Surgery --
Surface symbols --
Simplicial homology: --
Cycles and boundaries --
Homology groups --
Examples --
Simplicial maps --
Stellar subdivision --
Invariance --
Degree and Lefschetz number: --
Maps of spheres --
The Euler-Poincaré formula --
The Borsuk-Ulam theorem --
The Lefschetz fixed-point theorem --
Dimension --
Knots and covering spaces: --
Examples of knots --
The knot group --
Seifert surfaces --
Covering spaces --
The Alexander polynomial.
Series Title: Undergraduate texts in mathematics.
Responsibility: M.A. Armstrong.

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