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Principles of topology

Author: Fred H Croom
Publisher: Mineola, New York : Dover Publications, Inc., 2016. ©1989
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Croom, Fred H., 1941-
Principles of topology.
Mineola, New York : Dover Publications, Inc., 2016
(DLC) 2015030379
(OCoLC)916408939
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Fred H Croom
ISBN: 9780486810447 0486810445
OCLC Number: 945566540
Notes: Originally published: Philadelphia : Saunders College Publishing, 1989; slightly corrected.
Description: 1 online resource (xi, 312 pages)
Contents: Chapter 1. Introduction --
Chapter 2. The Line and the Plane --
Chapter 3. Metric Spaces --
Chapter 4. Topological Spaces 99 --
Chapter 5. Connectedness --
Chapter 6. Compactness --
Chapter 7. Product and Quotient Spaces --
Chapter 8. Separation Properties and Metrization --
Chapter 9. The Fundamental Group --
Appendix: Introduction to Groups --
Bibligraphy --
Index.
Responsibility: Fred H. Croom, the University of the South.

Abstract:

Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.

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