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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 3, Pages 417-421
http://dx.doi.org/10.1155/S0161171297000574

On strong form of Arzela convergence

Department of Mathematics, Pedagogical University, Arciszewskiego 22 b, Slupsk 76-200, Poland

Received 30 November 1995; Revised 23 April 1996

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.