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General Topology
An Introduction
-
Tom Richmond
Language:
English
Published/Copyright:
2020
About this book
The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.
- Applications of metrics include error-correcting codes and social choice.
- Pseudometrics, quasi-metrics, and partial metrics are explored.
- Connections between topology and order are examined.
- Over 740 exercises, from standard to novel, are included.
Author / Editor information
Tom Richmond, Western Kentucky University, USA.
Topics
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Frontmatter
I -
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Preface
V -
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Contents
IX -
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0. Preliminaries
1 -
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1. Topologies
21 -
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2. New topologies from existing topologies
65 -
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3. Continuity
85 -
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4. Connectedness
103 -
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5. Compactness
115 -
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6. Metric spaces and real analysis
133 -
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7. Separation axioms and compactifications
157 -
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8. Alexandroff spaces
181 -
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9. Lattice properties
201 -
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10. Partially ordered topological spaces
219 -
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11. Variations on metric spaces
233 -
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12. Uniform structures
253 -
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13. Continuous deformation of sets and curves
283 -
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Index
307 -
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Bibliography
313
Publishing information
Pages and Images/Illustrations in book
eBook published on:
July 6, 2020
eBook ISBN:
9783110686579
Paperback published on:
July 6, 2020
Paperback ISBN:
9783110686562
Pages and Images/Illustrations in book
Front matter:
12
Main content:
314
Illustrations:
83
Coloured Illustrations:
21
Tables:
5
Audience(s) for this book
Graduate and undergraduate students in Mathematics; researchers in Computer Science.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
