Geodesic
Remarks on r-separability of Pixley–Roy hyperspaces
Filomat, Tome 36 (2022) no. 3, p. 881

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DOI

Let PR(X) denote the hyperspace of nonempty finite subsets of a topological space X with the Pixley– Roy topology. In this paper, motivated by [4], we introduced c f-covers and rc f-covers of X to establish the R-selective separability and the M-selective separability in PR(X) under the Pixley–Roy topology. We proved that the following statements are equivalent for a space X: (1) PR(X) is R-separable (resp., M-separable); (2) X satisfies S 1 (C rc f , C rc f) (resp., S fin (C rc f , C rc f)); (3) X is countable and each co-finite subset of X satisfies S 1 (C c f , C c f) (resp., S fin (C c f , C c f)); (4) X is countable and PR(X) has countable strong fan tightness (resp., PR(X) has countable fan tightness)
DOI : 10.2298/FIL2203881L
Classification : 54B20, 54D20
Keywords: Pixley–Roy topology, R-separable, M-separable, co-finite set, c f -cover, rc f -cover 
Zuquan Li. Remarks on r-separability of Pixley–Roy hyperspaces. Filomat, Tome 36 (2022) no. 3, p. 881 . doi: 10.2298/FIL2203881L
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     author = {Zuquan Li},
     title = {Remarks on r-separability of {Pixley{\textendash}Roy} hyperspaces},
     journal = {Filomat},
     pages = {881 },
     year = {2022},
     volume = {36},
     number = {3},
     doi = {10.2298/FIL2203881L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2203881L/}
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