International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 417-421
doi:10.1155/S0161171297000574

On strong form of Arzela convergence

Abstract

We define some new type of convergence of nets of functions which is formulated in terms of open covers. It preserves continuity and under some assumptions implies (or coincides with) the Arzela quasi-uniform convergence. Furthermore, the introduced strong convergence is used for characterization of compactness and regularity of a topological space.