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Realcompactness of hyperspaces and extensions of open-closed maps

✍ Scribed by Haruto Ohta


Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
574 KB
Volume
17
Category
Article
ISSN
0166-8641

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DieudonnΓ© completeness of a space of clo
✍ Haruto Ohta πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 333 KB

We prove: if X is a paracompact Hausdorff space, then the space 2x of all nonempty closed subsets of X with the Vietoris topology is DieudonnC complete. If f : X -+ Y is an open-closed continuous onto map and 2 ~4~) is DieudonnC complete, then the extension p(f) : p(X) + p(Y) is open-closed, where p