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Proceedings of the American Mathematical Society

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

 

 

A hyperspace for convergence spaces


Author: R. J. Gazik
Journal: Proc. Amer. Math. Soc. 37 (1973), 234-240
MSC: Primary 54A20
DOI: https://doi.org/10.1090/S0002-9939-1973-0309042-1
MathSciNet review: 0309042
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Abstract: The purpose of this note is to introduce a convergence structure $ h(t)$ on the collection $ C(E)$ of nonempty, compact subsets of a Hausdorff convergence space (E, t). It is shown that if (E, t) is topological, then $ h(t)$ agrees with the Vietoris topology on $ C(E)$. It is proved that $ (C(E),h(t))$ is Hausdorff, that it inherits regularity from (E, t) and that it is compact whenever (E, t) is compact and regular.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0309042-1
Keywords: Convergence spaces, convergence structures, limit spaces, limit structures, Vietoris topology, directed sets, ultrafilters, cofinal segments, selections of cofinal segments
Article copyright: © Copyright 1973 American Mathematical Society