The classical fields are the real, rational, complex and p-adic
numbers. Each of these fields comprises several intimately
interwoven algebraical and topological structures. This
comprehensive volume analyzes the interaction and interdependencies
of these different aspects. The real and rational numbers are
examined additionally with respect to their orderings, and these
fields are compared to their non-standard counterparts. Typical
substructures and quotients, relevant automorphism groups and many
counterexamples are described. Also discussed are completion
procedures of chains and of ordered and topological groups, with
applications to classical fields. The p-adic numbers are placed in
the context of general topological fields: absolute values,
valuations and the corresponding topologies are studied, and the
classification of all locally compact fields and skew fields is
presented. Exercises are provided with hints and solutions at the
end of the book. An appendix reviews ordinals and cardinals,
duality theory of locally compact Abelian groups and various
constructions of fields.
General
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