Non-metrisable Manifolds

Authors: Gauld, David

  • The first dedicated book on understanding non-metrisable manifolds
  • The interesting boundary between metrisability and non-metrisability for a manifold is addressed
  • Highlights over 25 years of research on Manifolds/Topology
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eBook $84.99
price for USA in USD (gross)
  • ISBN 978-981-287-257-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-981-287-256-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-981-10-1152-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Manifolds fall naturally into two classes depending on whether they can be fitted with a distance measuring function or not. The former, metrisable manifolds, and especially compact manifolds, have been intensively studied by topologists for over a century, whereas the latter, non-metrisable manifolds, are much more abundant but have a more modest history, having become of increasing interest only over the past 40 years or so. The first book on this topic, this book ranges from criteria for metrisability, dynamics on non-metrisable manifolds, Nyikos’s Bagpipe Theorem and whether perfectly normal manifolds are metrisable to structures on manifolds, especially the abundance of exotic differential structures and the dearth of foliations on the long plane. A rigid foliation of the Euclidean plane is described. This book is intended for graduate students and mathematicians who are curious about manifolds beyond the metrisability wall, and especially the use of Set Theory as a tool.

Reviews

“The book is well-organized with two appendices: the first one collects all necessary topological results, and the second one provides preliminaries on set theory. In addition, each chapter has its own abstract and references. … this book is so-far the only monograph in the literature which gives a comprehensive treatment on non-metrizable manifolds. It is recommended to those readers who have general knowledge on manifolds as topological objects and are curious about what happens beyond the wall of metrizability.” (Jiling Cao, zbMATH 1336.57031, 2016)

“First of its kind, this volume by Gauld (Univ. of Auckland, New Zealand) both synthesizes and improves upon the journal literature, demonstrating clearly that non-metrizable manifolds admit profitable study from a variety of vantages (e.g., set theory, differential topology) and exhibit rich and surprising behaviors, using theory built on, but hardly reducible to, the metrizable case. … Summing Up: Highly recommended. Upper-division undergraduates through professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (2), October, 2015)


Table of contents (9 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-981-287-257-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-981-287-256-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-981-10-1152-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Non-metrisable Manifolds
Authors
Copyright
2014
Publisher
Springer Singapore
Copyright Holder
Springer Science+Business Media Singapore
eBook ISBN
978-981-287-257-9
DOI
10.1007/978-981-287-257-9
Hardcover ISBN
978-981-287-256-2
Softcover ISBN
978-981-10-1152-8
Edition Number
1
Number of Pages
XVI, 203
Number of Illustrations and Tables
45 b/w illustrations, 6 illustrations in colour
Topics