ABSTRACT

Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.

part I|94 pages

Survey of Topological Fields

chapter 1|8 pages

Introduction

chapter 2|19 pages

Valuations and Other Examples

chapter 3|11 pages

The Lattice of Ring Topologies

chapter 4|22 pages

Locally Bounded Fields

chapter 5|6 pages

Normed Fields

chapter 6|5 pages

Completeness

chapter 7|3 pages

Embedding and Extension

chapter 8|6 pages

Existence of Field Topologies

chapter 9|4 pages

Connected Fields

chapter 10|4 pages

Disconnected Fields

chapter 11|4 pages

Linear Fields

part II|69 pages

Valued Fields

chapter 12|15 pages

Absolute Values

chapter 13|4 pages

Places

chapter 14|16 pages

Vector Spaces and Strictly Minimal Fields

chapter 15|15 pages

Extensions of Valuations

chapter 16|17 pages

Characterizations