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An internal and an external characterization of convergence spaces in which adherences of filters are closed


Author: Eva Lowen-Colebunders
Journal: Proc. Amer. Math. Soc. 72 (1978), 205-210
MSC: Primary 54A05; Secondary 54A20
DOI: https://doi.org/10.1090/S0002-9939-1978-0500785-8
MathSciNet review: 0500785
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Abstract: The purpose of this note is to give necessary and sufficient conditions for a convergence space (X, q) such that for every filter on X its adherence is a closed subset of (X, q). An internal characterization of this property is given by weakening the diagonal condition of Kowalsky. An external characterization is given using a hyperspace structure on the collection of all closed subsets of the given space. It will be shown that a convergence space has closed adherences if and only if the hyperspace is compact.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0500785-8
Keywords: Convergence spaces, closed adherences, almost topological spaces, diagonal spaces, hyperspace
Article copyright: © Copyright 1978 American Mathematical Society

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