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Non-metrisable Manifolds by David Gauld at Abbey's Bookshop,
Non-metrisable Manifolds
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David Gauld

Non-metrisable Manifolds

David Gauld

$126.95   $101.37

Hardback

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English
Springer Verlag, Singapore
16 December 2014
Analytic geometry; Algebraic topology; Non-linear science
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.
By:  
Imprint:   Springer Verlag, Singapore
Country of Publication:   Singapore
Edition:   2014 ed.
Dimensions:   Height: 235mm,  Width: 155mm,  Spine: 14mm
Weight:   4.557kg
ISBN:   9789812872562
ISBN 10:   9812872566
Pages:   203
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

Reviews for Non-metrisable Manifolds

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)


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