Geodesic
Characterizations of weaker forms of the Rothberger and Menger properties in hyperspaces
Filomat, Tome 37 (2023) no. 15, p. 5053

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DOI

In this paper, we introduce the notions of almost π ∆ (Λ)-network and weakly π ∆ (Λ)-network to characterize the properties of almost Rothberger (Menger) and weakly Rothberger (Menger), respectively, in the hyperspaces CL(X), K(X), F(X) and CS(X), endowed with the hit-and-miss topology. Also, we introduce the concepts of groupable c ∆ (Λ)-cover and weakly (∆, Λ)-groupable cover of X to give equivalences of the selection principles S 1 (D, D p), S fin (D, D p), S 1 (D, D wp) and S fin (D, D wp) in the same hyperspaces.
DOI : 10.2298/FIL2315053C
Classification : 54B20, 54A05, 54A25, 54D20
Keywords: Almost Rothberger (Menger), Groupable cover, Hit-and-miss topologies, Hyperspaces, Selection principles, Weakly groupable cover, Weakly Rothberger (Menger) 
Ricardo Cruz-Castillo; Alejandro Ramírez-Páramo; Jesús F Tenorio. Characterizations of weaker forms of the Rothberger and Menger properties in hyperspaces. Filomat, Tome 37 (2023) no. 15, p. 5053 . doi: 10.2298/FIL2315053C
@article{10_2298_FIL2315053C,
     author = {Ricardo Cruz-Castillo and Alejandro Ram{\'\i}rez-P\'aramo and Jes\'us F Tenorio},
     title = {Characterizations of weaker forms of the {Rothberger} and {Menger} properties in hyperspaces},
     journal = {Filomat},
     pages = {5053 },
     year = {2023},
     volume = {37},
     number = {15},
     doi = {10.2298/FIL2315053C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2315053C/}
}
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