Function spaces and an Ascoli theorem in approach theory
by
Robert Lowen
University of Antwerp, RUCA
Coauthors: P. Wuyts

Making use not only of approach spaces but also of a uniform version of the theory we are able to define concepts such as equicontractivity and a measure of the Cauchyness of filters. Next we found out that there exists a natural approach uniformity on spaces of functions which has as underlying uniformity the well-known Bourbaki uniformity of S-convergence for a given cover S. Having all these concepts at our disposal we prove a general version of an Ascoli theorem in the context of approach theory.

Date received: April 6, 2001

Copyright © 2001 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 # cafw-74.