Geodesic
The quasi-Rothberger property of Pixley–Roy hyperspaces
Filomat, Tome 37 (2023) no. 8, p. 2531

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Let PR(X) denote the hyperspace of non-empty finite subsets of a topological space X with Pixley–Roy topology. In this paper, we investigate the quasi-Rothberger property in hyperspace PR(X). We prove that for a space X, the followings are equivalent: (1) PR(X) is quasi-Rothberger; (2) X satisfies S 1 (Π rc f −h , Π wrc f −h); (3) X is separable and each co-finite subset of X satisfies S 1 (Π pc f −h , Π wpc f −h); (4) X is separable and PR(Y) is quasi-Rothberger for each co-finite subset Y of X. We also characterize the quasi-Menger property and the quasi-Hurewicz property of PR(X). These answer the questions posted in [8].
DOI : 10.2298/FIL2308531L
Classification : 54B20, 54D20
Keywords: Pixley–Roy topology, selection principle, quasi-Rothberger, quasi-Menger, quasi-Hurewicz, rc f -network on a hit-family, weakly rc f -network on a hit-family 
Zuquan Li. The quasi-Rothberger property of Pixley–Roy hyperspaces. Filomat, Tome 37 (2023) no. 8, p. 2531 . doi: 10.2298/FIL2308531L
@article{10_2298_FIL2308531L,
     author = {Zuquan Li},
     title = {The {quasi-Rothberger} property of {Pixley{\textendash}Roy} hyperspaces},
     journal = {Filomat},
     pages = {2531 },
     year = {2023},
     volume = {37},
     number = {8},
     doi = {10.2298/FIL2308531L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2308531L/}
}
TY  - JOUR
AU  - Zuquan Li
TI  - The quasi-Rothberger property of Pixley–Roy hyperspaces
JO  - Filomat
PY  - 2023
SP  - 2531 
VL  - 37
IS  - 8
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2308531L/
DO  - 10.2298/FIL2308531L
LA  - en
ID  - 10_2298_FIL2308531L
ER  - 
%0 Journal Article
%A Zuquan Li
%T The quasi-Rothberger property of Pixley–Roy hyperspaces
%J Filomat
%D 2023
%P 2531 
%V 37
%N 8
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2308531L/
%R 10.2298/FIL2308531L
%G en
%F 10_2298_FIL2308531L

Cité par Sources :