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OverviewManifolds 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. Full Product DetailsAuthor: David GauldPublisher: Springer Verlag, Singapore Imprint: Springer Verlag, Singapore Edition: Softcover reprint of the original 1st ed. 2014 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 3.401kg ISBN: 9789811011528ISBN 10: 9811011524 Pages: 203 Publication Date: 23 August 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsThe 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) 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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |