Topology

Başlık:

Topology

Yazar:

Manetti, Marco. author.

ISBN:

9783319169583

Ek Yazar:

Manetti, Marco. author.

Fiziksel Tanım:

XII, 309 p. 72 illus. online resource.

Series:

UNITEXT, 91

Contents:

1 Geometrical introduction to topology -- 2 Sets -- 3 Topological structures -- 4 Connectedness and compactness -- 5 Topological quotients -- 6 Sequences -- 7 Manifolds, infinite products and paracompactness -- 8 More topics in general topology -- 9 Intermezzo -- Homotopy -- 10 The fundamental group -- 11 Covering spaces -- Monodromy -- 12 van Kampen's theorem -- 13 Selected topics in algebraic topology -- 14 Hints and solutions -- 15 References -- 16 Index.

Abstract:

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

Konu Terimleri:

Mathematics.

Algebraic topology.

Mathematics, general.

Added Corporate Author:

SpringerLink (Online service)

Electronic Access:

http://dx.doi.org/10.1007/978-3-319-16958-3

Mevcut:*

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	E-Kitap	79533-1001	QA612 -612.8	Searching... Unknown

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Özet

The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

Author Notes

Prof. Marco Manetti , Dipartimento di Matematica "Guido Castelnuovo", Sapienza - Università di Roma, Roma, Italy.

Reviews (1)

Choice Review

In writing this book, Manetti followed the expository strategy of many topology textbooks written well after John Kelley's classic General Topology (1955). Manetti devotes roughly equal space to general topology and to algebraic topology (or, at least, to the homotopy-theoretic component thereof). The intrepid reader "studying on this book" will encounter full proofs of most of the theorems presented; illuminating figures and illustrations; some 500 or so exercises to be solved ("with dedication," as the author urges); and assorted linguistic idiosyncrasies inevitably present when an Italian original is rendered into English by a Brazilian translator. But it is all good fun. The first 8 of the 15 bite-sized chapters are on the point-set-theoretic side of the topological realm; the remaining 7 are on the algebraic side; a last chapter offers "hints and solutions" for selected exercises. Many of the chapters close with a brief list of relevant references. Summing Up: Recommended. Upper-division undergraduates; graduate students. --Fred E. J. Linton, Wesleyan University