Geodesic
Variations of star selection principles on small spaces
Filomat, Tome 36 (2022) no. 14, p. 4903

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DOI

In this work, we introduce the notions of Star-σK and absolutely Star-σK spaces which allow us to unify results among several properties in the theory of star selection principles on small spaces. In particular, results on star selective versions of the Menger, Hurewicz and Rothberger properties and selective versions of property (a) regarding the size of the space. Connections to other well-known star properties are mentioned. Furthermore, the absolute and selective version of the neighbourhood star selection principle are introduced. As an application, it is obtained that the extent of a separable absolutely strongly star-Menger (absolutely strongly star-Hurewicz) space is at most the dominating number d (the bounding number b).
DOI : 10.2298/FIL2214903C
Classification : 54D20, 54A25
Keywords: (Absolutely) strongly star Menger, absolutely neighbourhood star Menger, Hurewicz, Rothberger, Lindelöf, selectively (a), star selection principles 
Javier Casas-De La Rosa; Sergio A Garcia-Balan. Variations of star selection principles on small spaces. Filomat, Tome 36 (2022) no. 14, p. 4903 . doi: 10.2298/FIL2214903C
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