Springer celebrates 175 years of publishing excellence! Join us >>

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
see more benefits

Buy this book

eBook 71,39 €
price for Spain (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 88,39 €
price for Spain (gross)
  • ISBN 978-981-287-256-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-981-10-1152-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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)

  • Topological Manifolds

    Gauld, David

    Pages 1-19

    Preview Buy Chapter 30,19 €
  • Edge of the World: When Are Manifolds Metrisable?

    Gauld, David

    Pages 21-36

    Preview Buy Chapter 30,19 €
  • Geometric Tools

    Gauld, David

    Pages 37-48

    Preview Buy Chapter 30,19 €
  • Type I Manifolds and the Bagpipe Theorem

    Gauld, David

    Pages 49-62

    Preview Buy Chapter 30,19 €
  • Homeomorphisms and Dynamics on Non-metrisable Manifolds

    Gauld, David

    Pages 63-86

    Preview Buy Chapter 30,19 €

Buy this book

eBook 71,39 €
price for Spain (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 88,39 €
price for Spain (gross)
  • ISBN 978-981-287-256-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-981-10-1152-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

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