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- Title
A note on κ-Fréchet-Urysohn property in function spaces.
- Authors
Tkachuk, V. V.
- Abstract
We establish that a Tychonoff space X has the property (κ) if all countable subsets of X are scattered. Therefore a countably compact space X does not need to be scattered if Cp(X) is κ -Fréchet-Urysohn. However, if a hereditarily Baire space is sequential and has the property (κ), then it must be scattered. We also prove, for any space X, that Cp(X) is κ -Fréchet-Urysohn if and only if so is Cp(X,[0, 1]). A pseudocompact first countable space must be scattered if it has the property (κ).
- Subjects
FUNCTION spaces; BAIRE spaces; COMPACT spaces (Topology)
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2021, Vol 28, Issue 1, p123
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/j.bbms.200704