Geodesic
The weakly Rothberger property of Pixley–Roy hyperspaces
Filomat, Tome 36 (2022) no. 16, p. 5493

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DOI

Let PR(X) denote the hyperspace of nonempty finite subsets of a topological space X with Pixley– Roy topology. In this paper, by introducing closed-miss-finite networks and using principle ultrafilters, we proved that the following statements are equivalent for a space X: (1) PR(X) is weakly Rothberger; (2) X satisfies S 1 (Π rc f , Π wrc f); (3) X is separable and X − {x} satisfies S 1 (Π c f , Π wc f) for each x ∈ X; (4) X is separable and each principal ultrafilter F [x] in PR(X) is weakly Rothberger in PR(X). We also characterize the weakly Menger property and the weakly Hurewicz property of PR(X).
DOI : 10.2298/FIL2216493L
Classification : 54B20, 54D20
Keywords: Pixley–Roy topology, weakly Rothberger, weakly Menger, weakly Hurewicz, principal ultrafilter, c f -network, rc f - network, weakly c f -network, weakly rc f -network 
Zuquan Li. The weakly Rothberger property of Pixley–Roy hyperspaces. Filomat, Tome 36 (2022) no. 16, p. 5493 . doi: 10.2298/FIL2216493L
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     author = {Zuquan Li},
     title = {The weakly {Rothberger} property of {Pixley{\textendash}Roy} hyperspaces},
     journal = {Filomat},
     pages = {5493 },
     year = {2022},
     volume = {36},
     number = {16},
     doi = {10.2298/FIL2216493L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2216493L/}
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