International Journal of Mathematics and Mathematical Sciences (Jan 1997)

On strong form of Arzela convergence

  • Janina Ewert

DOI
https://doi.org/10.1155/s0161171297000574
Journal volume & issue
Vol. 20, no. 3
pp. 417 – 421

Abstract

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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.

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