A Guide to Topology

by Krantz, Steven G.

• ISBN13: 9780883853467
• ISBN10: 0883853469
• Format: Hardcover
• Copyright: 2009-07-16
• Publisher: Mathematical Assn of Amer

Summary

A Guide to Topology is an introduction to basic topology for graduate or advanced undergraduate students. It covers point-set topology, Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Students studying for exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.

Author Biography

Gerald B. Folland received his bachelor's degree from Harvard University in 1968 and his doctorate from Princeton University in 1971. After two years at the Courant Institute, he moved to the University of Washington, where he is now professor of mathematics. He is the author of ten textbooks and research monographs in the areas of real analysis, harmonic analysis, partial differential equations, and mathematical physics.

Table of Contents

Preface

Fundamentals

What is topology?

First definitions

Mappings

The separation axioms

Compactness

Homeomorphisms

Connectedness

Path-connectedness

Continua

Totally disconnected spaces

The Cantor set

Metric spaces

Metrizability

Baire's theorem

Lebesgue's lemma and Lebesgue numbers

Advanced Properties

Basis and subbasis

Product spaces

Relative topology

First countable and second countable

Compactifications

Quotient topologies

Uniformities

Morse theory

Proper mappings

Paracompactness

Moore-Smith Convergence and Nets

Introductory remarks

Nets

Function Spaces

Preliminary ideas

The topology of pointwise convergence

The compact-open topology

Uniform convergence

Equicontinuity and the Ascoli-Arzela theorem

The Weierstrass approximation theorem

Table of notation

Glossary

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.