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- W4320725619 abstract "We show that exponential separability is an inverse invariant of closed maps with countably compact exponentially separable fibers. This implies that it is preserved by products with a scattered compact factor and in the products of sequential countably compact spaces. We also provide an example of a $sigma$-compact crowded space in which all countable subspaces are scattered. If $X$ is a Lindelöf space and every $Ysubset X$ with $|Y|leq 2^{omega_1}$ is scattered, then $X$ is functionally countable; if every $Ysubset X$ with $|Y|leq 2^{mathfrak{c}} $ is scattered, then $X$ is exponentially separable. A Lindelöf $Sigma$-space $X$ must be exponentially separable provided that every $Ysubset X$ with $|Y|leq {mathfrak{c}}$ is scattered. Under the Luzin axiom ($2^{omega_1}>{mathfrak{c}} $) we characterize weak exponential separability of $C_p(X,[0,1])$ for any metrizable space $X$. Our results solve several published open questions." @default.
- W4320725619 created "2023-02-15" @default.
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- W4320725619 date "2023-02-14" @default.
- W4320725619 modified "2023-09-30" @default.
- W4320725619 title "Exponential separability is preserved by some products" @default.
- W4320725619 doi "https://doi.org/10.14712/1213-7243.2022.021" @default.
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