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Conference in Honor of Alexander Arhangelskii
June 29 - July 3, 2003
Brooklyn College of the City University of New York
Brooklyn, NY, USA

Organizers
Raushan Buzyakova, Ralph Kopperman, Gerald Itzkowitz, Raymond Gittings, Susan Andima, Oleg Pavlov, Oleg Okunev, Dennis Burke, Vladimir Uspenskii, Witold Marciszewski, Stephen Watson, Hans-Peter Kunzi

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Decompositions of UC-spaces: destroy uniform continuity and preserve continuity
by
Giuseppe Di Maio
Dipartimento di Matematica, SUN; Via A. Vivaldi , 43; I-8110 Caserta; Italy
Coauthors: Enrico Meccariello, Somashekhar Naimpally

UC spaces are the metric spaces in which continuous (real valued) functions are uniformly continuous. We introduce a new class of spaces , called CU spaces, in which Cauchy maps are uniformly continuous.The result UC = complete + CU provides a decomposition of UC spaces. Moreover, we find characterizations of complete spaces and CU spaces parallel to those known for UC spaces. Actually, by using simple facts from Analysis, we show that is possible to destroy uniform continuity and preserve continuity in just two ways. The subject, with appropriate changes, could be taught to Calculus I students.

Date received: February 26, 2003

Copyright © 2003 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 # cajv-06.