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Topological Spaces : From Distance to Neighborhood - Gerard Buskes

Topological Spaces

From Distance to Neighborhood

Hardcover

Published: 15th August 1997
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gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Preface
The Line and the Plane
What Topology is about
Axioms for R
Convergent sequences and continuity
Curves in the plane
Metric Spaces
Metrics
Open and closed sets
Completeness
Uniform convergence
Sequential compactness
Convergent nets
Transition to Topology
Topological Spaces
Topological spaces
Compactness and the Hausdorff property
Products and quotients
The Hahn-Tietze-Tong-Urysohn Theorems
Connectedness
Tychonoff's Theorem
Postscript
A Smorgasbord for further study
Countable sets
A Farewell to the Reader
Literature
Index of Symbols
Index of Terms
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387949949
ISBN-10: 0387949941
Series: Undergraduate Texts in Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 313
Published: 15th August 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.42