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.

Keywords

• Arzela convergence
• almost compact space
• uniform space.