Topological Fields

Seth Warner (Eds.)0444874291, 9780444874290, 9780080872681

Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields). The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.

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Table of contents :
Content:
Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Foreword
Pages vii-ix

Notation
Pages ix-x

Chapter I Topological Groups
Pages 1-76

Chapter II Topological Rings and Modules
Pages 77-136

Chapter III Absolute Values
Pages 137-205

Chapter IV Topological Vector Spaces and Their Applications
Pages 207-273

Chapter V Valuations
Pages 275-380

Chapter VI Locally Bounded Topologies
Pages 381-468

Chapter VII Historical Notes
Pages 469-509

Bibliography
Pages 511-548

Name Index
Pages 549-553

Subject Index
Pages 555-563