Non-metrisable Manifolds

David Gauld (Autor)

Buch | Softcover

203 Seiten

2016 | Softcover reprint of the original 1st ed. 2014
Springer Verlag, Singapore
978-981-10-1152-8 (ISBN)

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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.

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.

Erscheinungsdatum	13.08.2016
Zusatzinfo	6 Illustrations, color; 45 Illustrations, black and white; XVI, 203 p. 51 illus., 6 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Optik
Schlagworte	Bagpipe Theorem • Brown’s Monotone Union Theorem • Continuum Hypothesis • Dynamics on Manifolds • Exotic Structures on Long Plane • Foliations of the Plane • Foliations on Manifolds • Handlebody • Long Line • Metrisability Criteria for Manifolds • Non-Hausdorff Manifolds • Non-metrisable Manifolds • Perfect Normality versus Metrisability • Prüfer Manifold • Smooth manifolds • Type I Manifold
ISBN-10	981-10-1152-4 / 9811011524
ISBN-13	978-981-10-1152-8 / 9789811011528
Zustand	Neuware