Non-metrisable Manifolds

  • David Gauld

Table of contents

  1. Front Matter
    Pages i-xvi
  2. David Gauld
    Pages 1-19
  3. David Gauld
    Pages 37-48
  4. David Gauld
    Pages 101-127
  5. David Gauld
    Pages 129-152
  6. David Gauld
    Pages 153-166
  7. Back Matter
    Pages 167-203

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • David Gauld
    • 1
  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-287-257-9
  • Copyright Information Springer Science+Business Media Singapore 2014
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-287-256-2
  • Online ISBN 978-981-287-257-9
  • About this book
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