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On the Theory of Ultrametric Spaces
by
Sibylla Priess-Crampe
Universität Muenchen
Coauthors: Sibylla Priess-Crampe
This theory has different sources:
the theory of valuations and semivaluations (partially ordered value sets),
a very general Banach-like fixed point theorem and the theory of ordered groups.
An ultrametric space (X, d, \Gamma) is a set X, together with a partially
ordered set \Gamma which has a smallest element 0 and a distance function
d: X ×X --> \Gamma.
The distance function has similar properties as a metric but instead of
the triangle inequality it fulfills the following condition:
if d(x, y) <= \gamma and d(y, z) <= \gamma, then also d(x, z) <= \gamma.
We shall study for these spaces some of the concepts and theorems
which are of special importance in the theory of valued fields,
respectively ordered groups.
Date received: April 12, 1996
Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaf-64.