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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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A hyperspace for convergence spaces
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by R. J. Gazik
Proc. Amer. Math. Soc. 37 (1973), 234-240
DOI: https://doi.org/10.1090/S0002-9939-1973-0309042-1

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.
References
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Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • 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