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25 Remote Warehouse Mathematics- Topology

A Taste of Topology

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A Taste of Topology Cover

 

Synopses & Reviews

Publisher Comments:

If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students can benefit from some parts. Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * Nets are used extensively, in particular for an intuitive proof of  Tychonoff's theorem; * A short and elegant, but little known proof for the Stone-Weierstrass theorem is given.

Synopsis:

Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.

Synopsis:

This should be a revelation for mathematics undergraduates. Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.

Table of Contents

Preface.- Introduction.- Set Theory.- Metric Spaces.- Set Theoretic Topology.- Systems of Continuous Functions.- Basic Algebraic Topology.- The Classical Mittag-Leffler Theorem Derived from Bourbaki's.- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces.- The Arzela-Ascoli Theorem.- References.- List of Symbols.- Index.

Product Details

ISBN:
9780387257907
Author:
Runde, Volker
Publisher:
Springer
Author:
Cram101 Textbook Reviews
Subject:
Geometry - General
Subject:
Topology
Subject:
Topology - General
Subject:
MATHEMATICS / Topology
Subject:
Education-General
Subject:
Algebraic topology
Copyright:
Edition Number:
1
Edition Description:
1st ed. 2005. Corr. 2nd printing
Series:
Universitext
Publication Date:
July 2005
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
192
Dimensions:
235 x 155 mm 600 gr

Related Subjects

History and Social Science » Economics » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Mathematics » Topology

A Taste of Topology New Trade Paper
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Product details 192 pages Springer - English 9780387257907 Reviews:
"Synopsis" by , Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.
"Synopsis" by , This should be a revelation for mathematics undergraduates. Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.
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