Springer Monographs in Mathematics

Geometric Aspects of General Topology

Authors: Sakai, Katsuro

  • The perfect book for acquiring fundamental knowledge of simplicial complexes and the theories of dimension and retracts
  • Many proofs are illustrated by figures or diagrams for easier understanding
  • Fascinating problems in the final chapter enable readers to understand how deeply related the theories of dimension and retracts are
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  • ISBN 978-4-431-54397-8
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Hardcover $149.00
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  • ISBN 978-4-431-54396-1
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Softcover $149.00
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  • ISBN 978-4-431-54699-3
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About this book

This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars.

Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are.

Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.

About the authors

Katsuro Sakai Associate Professor University of Tsukuba, Institute of Mathematics Academic Degrees •Bachelor of Science—Nagoya University, March 1972 •Master of Science—Tokyo University of Education, March 1974 •Doctor of Science—University of Tsukuba, October 1979

Reviews

From the book reviews:

“This excellent book is designed for different graduate courses in geometric topology, as well as in general topology. At the same time it contains complete proofs of results interesting also for the specialist in geometric topology … .” (Vesko Valov, Mathematical Reviews, September, 2014)


Table of contents (7 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-4-431-54397-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-4-431-54396-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-4-431-54699-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Aspects of General Topology
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2013
Publisher
Springer Japan
Copyright Holder
Springer Japan
eBook ISBN
978-4-431-54397-8
DOI
10.1007/978-4-431-54397-8
Hardcover ISBN
978-4-431-54396-1
Softcover ISBN
978-4-431-54699-3
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XV, 521
Number of Illustrations and Tables
78 b/w illustrations
Topics