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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An internal and an external characterization of convergence spaces in which adherences of filters are closed
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by Eva Lowen-Colebunders PDF
Proc. Amer. Math. Soc. 72 (1978), 205-210 Request permission

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.
References
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • 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