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Non-metrisable manifolds

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 manifol...

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Detalles Bibliográficos
Autor principal: Gauld, David
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-981-287-257-9
http://cds.cern.ch/record/1980581
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author Gauld, David
author_facet Gauld, David
author_sort Gauld, David
collection CERN
description 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.
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spelling cern-19805812021-04-21T20:38:11Zdoi:10.1007/978-981-287-257-9http://cds.cern.ch/record/1980581engGauld, DavidNon-metrisable manifoldsMathematical Physics and Mathematics 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.Springeroai:cds.cern.ch:19805812014
spellingShingle Mathematical Physics and Mathematics
Gauld, David
Non-metrisable manifolds
title Non-metrisable manifolds
title_full Non-metrisable manifolds
title_fullStr Non-metrisable manifolds
title_full_unstemmed Non-metrisable manifolds
title_short Non-metrisable manifolds
title_sort non-metrisable manifolds
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-981-287-257-9
http://cds.cern.ch/record/1980581
work_keys_str_mv AT gaulddavid nonmetrisablemanifolds