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- W2031031693 abstract "Let γ and κ be infinite cardinals and λ a cardinal. A subspace A of a space X is said to be P γ (locally-finite)-embedded in X if every locally finite partition of unity with cardinality ⩽ γ on A can be extended to a locally finite partition of unity on X ; this extension property was defined by Dydak recently. In this paper, introducing a space J γ ( κ ) and a class of spaces called spaces of type t ( γ , κ , λ ), we characterize P γ (locally-finite)-embedding by products with these spaces. We also characterize extendability of locally finite κ + -open covers U of a closed subspace A of a normal space X to those of X by products with these spaces; this extends Przymusiński's result in 1984 of the case | U |=ω . We apply this result to give characterizations of functionally Katětov spaces and Katětov spaces by rectangular normality of products with these spaces." @default.
- W2031031693 created "2016-06-24" @default.
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- W2031031693 date "2002-07-01" @default.
- W2031031693 modified "2023-09-27" @default.
- W2031031693 title "P(locally-finite)-embedding and rectangular normality of product spaces" @default.
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- W2031031693 doi "https://doi.org/10.1016/s0166-8641(01)00162-6" @default.
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