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Lindelöf $P$-spaces need not be Sokolov

In: Mathematica Slovaca, vol. 67, no. 1
Vladimir V. Tkachuk
Detaily:
Rok, strany: 2017, 227 - 234
Kľúčové slová:
Lindelöf $P$-space, $\o$-modification, retraction, extent, scattered space, Eberlein compact space, Sokolov space, function space
O článku:
We show that for every Lindelöf $P$-space a weaker version of the Sokolov property holds. Besides, if $K$ is a scattered Eberlein compact space and $X$ is obtained from $K$ by declaring open all $G_\delta$-subsets of $K$, then $X$ is monotonically Sokolov. The proof of this statement uses the fact that every Lindelöf subspace of a scattered Eberlein compact space must be $\sigma$-compact; this result seems to be interesting in itself. We also give an example of a Lindelöf $P$-space $X$ such that $C_p(X)$ has uncountable extent. In particular, neither $X$ nor $C_p(X)$ has the Sokolov property.
Ako citovať:
ISO 690:
Tkachuk, V. 2017. Lindelöf $P$-spaces need not be Sokolov. In Mathematica Slovaca, vol. 67, no.1, pp. 227-234. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0262

APA:
Tkachuk, V. (2017). Lindelöf $P$-spaces need not be Sokolov. Mathematica Slovaca, 67(1), 227-234. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0262
O vydaní:
Publikované: 1. 2. 2017