International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 417-421
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 Janina Ewert. 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.
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.