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IV Iberoamerican Conference on Topology and its Applications (IV CITA)
April 18-21, 2001
University of Coimbra
Coimbra, Portugal

Organizers
Maria Manuel Clementino, Jorge Picado, Lurdes Sousa, Maria João Ferreira, Gonçalo Gutierres, Dirk Hofmann

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Uniformizing \Delta proximal topologies
by
G. Di Maio
Seconda Università degli Studi di Napoli, Caserta, Italy
Coauthors: E. Meccariello (Università del Sannio, Benevento, Italy), S. Naimpally (Toronto, Canada)

Beer and Tamaki investigated the necessary and sufficient conditions for the uniformizability of (proximal) \Delta-topologies.

Their proofs involved construction of special Urysohn functions. In this paper we use an new approach and show that every uniformizable (proximal) \Delta-topology is essentially a uniform topology with reference to a Hausdorff uniformity patterned after the one related to the Attouch-Wets topology. We also study \DeltaU-topologies, proximal \DeltaU-topologies which are obvious generalizations of the U-topology discovered by Costantini-Vitolo.

Date received: February 24, 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-28.