Topology Point-Set and Geometric

by Shick, Paul L.

• ISBN13: 9780470096055
• ISBN10: 0470096055
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-02-09
• Publisher: Wiley-Interscience

Summary

This text covers the essentials of point-set topology in a relatively terse presentation, with lots of examples and motivation along the way. Along with the standard point-set topology topics (connected spaces, compact spaces, separation axioms, and metric spaces), the author includes path-connectedness, and a chapter on constructing spaces from other spaces (including products, quotients, etc.). The text culminates in to two main chapters, each independent of the other: 1) The Classification Theorem for Compact, Connected Surfaces and 2) Fundamental Groups and Covering Spaces, with Applications giving the reader the choice of which subject best suits them.

Author Biography

PAUL L. SHICK, PhD, is Professor in the Department of Mathematics and Computer Science at John Carroll University in Cleveland, Ohio. He earned a PhD in Mathematics from Northwestern University in 1984, working in the area of stable homotopy theory. He remains active in research in algebraic topology.

Table of Contents

Foreword

Acknowledgments

Introduction: Intuitive Topology

Background on Sets and Functions

Topological Spaces

More on Open and Closed Sets and Continuous Functions

New Spaces from Old

Connected Spaces

Compact Spaces

Separation Axioms

Metric Spaces

The Classification of Surfaces

Fundamental Groups and Covering Spaces

References

Index

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