Ebook: Topologies and Uniformities

This book is based on lectures I have given to senior undergraduate and graduate audiences at Oxford and elsewhere over the years. My aim has been to provide an outline of both the topological theory and the uniform theory, with an emphasis on the relation between the two. Although I hope that the prospective specialist may find it useful as an introduction it is the non-specialist I have had more in mind in selecting the contents. Thus I have tended to avoid the ingenious examples and counterexamples which often occupy much of the space in books on general topology, and I have tried to keep the number of definitions down to the essential minimum. There are no particular prerequisites but I have worked on the assumption that a potential reader will already have had some experience of working with sets and functions and will also be familiar with the basic concepts of algebra and analysis. An earlier version of the present book appeared in 1987 under the title Topo­ logical and Uniform Spaces. When the time came for a new edition I came to the conclusion that, rather than just making the necessary corrections, it would be better to make more substantial alterations. Parts of the text have been rewritten and new material, including new diagrams, added.

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This book is a substantially revised edition of the UTM book: ISBN 0 387 96466-5, which is rewritten with a view to making the book far more accessible for undergraduates, particularly in the UK and Ireland. It contains more detailed explanations and ex ercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.

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This book is a substantially revised edition of the UTM book: ISBN 0 387 96466-5, which is rewritten with a view to making the book far more accessible for undergraduates, particularly in the UK and Ireland. It contains more detailed explanations and ex ercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.
Content:
Front Matter....Pages i-xv
Topological Spaces....Pages 1-27
Continuity....Pages 29-46
The Induced Topology and Its Dual....Pages 47-61
Open Functions and Closed Functions....Pages 63-73
Compact Spaces....Pages 75-86
Separation Conditions....Pages 87-102
Uniform Spaces....Pages 103-125
The Uniform Topology....Pages 127-144
Connectedness....Pages 145-164
Countability and Related Topics....Pages 165-177
Functional Separation Conditions....Pages 179-188
Completeness and Completion....Pages 189-201
Back Matter....Pages 203-230

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This book is a substantially revised edition of the UTM book: ISBN 0 387 96466-5, which is rewritten with a view to making the book far more accessible for undergraduates, particularly in the UK and Ireland. It contains more detailed explanations and ex ercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.
Content:
Front Matter....Pages i-xv
Topological Spaces....Pages 1-27
Continuity....Pages 29-46
The Induced Topology and Its Dual....Pages 47-61
Open Functions and Closed Functions....Pages 63-73
Compact Spaces....Pages 75-86
Separation Conditions....Pages 87-102
Uniform Spaces....Pages 103-125
The Uniform Topology....Pages 127-144
Connectedness....Pages 145-164
Countability and Related Topics....Pages 165-177
Functional Separation Conditions....Pages 179-188
Completeness and Completion....Pages 189-201
Back Matter....Pages 203-230
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