Decomposition of UC-spaces II: the uniform case
by
Enrico Meccariello
Facoltà di Ingegneria, Università del Sannio, Palazzo Bosco Lucarelli, Piazza Roma, 82100-Benevento; Italy
Coauthors: Giuseppe Di Maio, Somashekhar Naimpally

There is a considerable literature on UC-metric or UC-uniform spaces, i.e. spaces in which continuity equals uniform continuity. We show this topic in depth using proximity and the authors' recent work concerning decomposition of UC-metric spaces. We study this problem in Tychonoff spaces endowed with a uniformity and a proximity where proximal continuity and uniform continuity are not equivalent as in metric spaces. So in this setting the solution to the UC problem is more intricate than in metric spaces. We introduce a new proximity, called Cauchy or C-proximity, and characterize complete uniform spaces in terms of two proximities.

Date received: March 13, 2003