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Some Results on the Countable Compactness and Pseudocompactness of Hyperspaces

Published online by Cambridge University Press:  20 November 2018

John Ginsburg
John Ginsburg*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Let X be a Hausdorff space. Let 2X denote the set of all non-empty closed subsets of X. For a subset A of X, we set 2A = {F 6 2X : F ⊆ A}. Recall that the finite topology on 2X is that topology having as a sub-basis the family {2G : G is open in X} U }2X — 2F : F is closed in X). When endowed with this topology, 2X is referred to as the hyper space of X. For the fundamental properties of hyperspaces, we refer the reader to [6; 7]. Following [6], we adopt the following notation: If A0, A1, … , An are subsets of X, we set and for all .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 6 , 01 December 1975 , pp. 1392 - 1399
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bernstein, A. R., A new kind of compactness for topological spaces, Fund. Math. 66 (1970), 185–193.Google Scholar
2. Frolik, Z., Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87–91 Google Scholar
3. Ganea, T., Symmetrische Potenzen topologischer Raume, Math. Nachr. 11 (1954), 305–316.Google Scholar
4. Ginsburgand, J. Saks, V., Some applications of ultrafilters in topology, Pac. J. Math. 57 (1975).Google Scholar
5. Keesling, J., Normality and properties related to compactness in hyperspaces, Proc. Amer. Math. Soc. 24 (1970), 760–766.Google Scholar
6. Kuratowski, K., Topology I (Academic Press, 1966).Google Scholar
7. Michael, E., Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152–182.Google Scholar