Generalized ultrametric spaces, valued and semivalued groups arising from the theory of shape
by
Manuel Alonso Morón
Universidad Politécnica de Madrid
Coauthors: F. R. Ruiz del Portal

In a series of papers we have conceived and developed some connections between non-Archimedean metrics and the theory of shape for compact metric spaces. After doing this, we found out some recent results generalizing the concept of an ultrametric by means of changing the real line by any partially ordered set. In this talk we point out that this is an adequate framework to extend our results to the theory of shape for arbitrary topological spaces. We are able, in particular, to give a natural structure of valued or semivalued group on the shape groups and the groups of shape equivalences.

Date received: February 10, 1997

Copyright © 1997 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 # caak-33.