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
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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.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