Theodore W. Gamelin, Robert Everist Greene

Introduction to Topology (eBook, ePUB)

Second Edition

• Format: ePub

Produktbeschreibung

One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics.
While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point-set topology material is treated in the first two chapters; algebraic topological material in the remaining two. The authors lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Second, the treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proof of some highly nontrivial results. By presenting homotopy theory without considering homology theory, important applications become immediately evident without the necessity of a large formal program.
Prerequisites are familiarity with real numbers and some basic set theory. Carefully chosen exercises are integrated into the text (the authors have provided solutions to selected exercises for the Dover edition), while a list of notations and bibliographical references appear at the end of the book.

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Produktdetails

• Verlag: Dover Publications
• Seitenzahl: 256
• Erscheinungstermin: 22. April 2013
• Englisch
• ISBN-13: 9780486320182
• Artikelnr.: 39547282

Inhaltsangabe

ONE METRIC SPACES 1 Open and closed sets 2 Completeness 3 The real line 4
Products of metric spaces 5 Compactness 6 Continuous functions 7 Normed
linear spaces 8 The contraction principle 9 The Frechet derivative TWO
TOPOLOGICAL SPACES 1 Topological spaces 2 Subspaces 3 Continuous functions
4 Base for a topology 5 Separation axioms 6 Compactness 7 Locally compact
spaces 8 Connectedness 9 Path connectedness 10 Finite product spaces 11 Set
theory and Zorn's lemma 12 Infinite product spaces 13 Quotient spaces THREE
HOMOTOPY THEORY 1 Groups 2 Homotopic paths 3 The fundamental group 4
Induced homomorphisms 5 Covering spaces 6 Some applications of the index 7
Homotopic maps 8 Maps into the punctured plane 9 Vector fields 10 The
Jordan Curve Theorem FOUR HIGHER DIMENSIONAL HOMOTOPY 1 Higher homotopy
groups 2 Noncontractibility of Sn 3 Simplexes and barycentric subdivision 4
Approximation by piecewise linear maps 5 Degrees of maps BIBLIOGRAPHY LIST
OF NOTATIONS SOLUTIONS TO SELECTED EXERCISES INDEX