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Non-metrisable Manifolds
David Gauld
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Naturwissenschaften, Medizin, Informatik, Technik / Geometrie
Beschreibung
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.
Kundenbewertungen
Non-Hausdorff Manifolds, Prüfer Manifold, Long Line, Dynamics on Manifolds, Exotic Structures on Long Plane, Foliations on Manifolds, Continuum Hypothesis, Non-metrisable Manifolds, Bagpipe Theorem, Metrisability Criteria for Manifolds, Type I Manifold, Brown’s Monotone Union Theorem, Foliations of the Plane, Smooth Manifolds, Handlebody, Perfect Normality versus Metrisability