On strong form of Arzela convergence

Janina Ewert

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-5

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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:835409

DOI: 10.1155/S0161171297000574

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