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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

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