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＜電子ブック＞
Non-metrisable Manifolds / by David Gauld

版	1st ed. 2014.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XVI, 203 p. 51 illus., 6 illus. in color : online resource
著者標目	*Gauld, David author SpringerLink (Online service)
件　名	LCSH:Manifolds (Mathematics) LCSH:Nonlinear Optics LCSH:Algebraic topology FREE:Manifolds and Cell Complexes FREE:Nonlinear Optics FREE:Algebraic Topology
一般注記	Topological Manifolds -- Edge of the World: When are Manifolds Metrisable? -- Geometric Tools -- Type I Manifolds and the Bagpipe Theorem -- Homeomorphisms and Dynamics on Non-Metrisable Manifolds -- Are Perfectly Normal Manifolds Metrisable? -- Smooth Manifolds -- Foliations on Non-Metrisable Manifolds -- Non-Hausdorff Manifolds and Foliations 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 HTTP:URL=https://doi.org/10.1007/978-981-287-257-9

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