Iterations and unions of star selection properties on topological spaces

Year 2024, Early Access, 1 - 20

Javier Casas-de La Rosa , William Chen-mertens Sergio A. Garcia-balan

https://doi.org/10.15672/hujms.1198061

Abstract

In this paper, we investigate what selection principles properties are possessed by small (with respect to the bounding and dominating numbers) unions of spaces with certain (star) selection principles.. Furthermore, we give several results about iterations of these properties and weaker properties than paracompactness. In addition, we study the behaviour of these iterated properties on $\Psi$-spaces. Finally, we show that, consistently, there is a normal star-Menger space that is not strongly star-Menger; this example answers a couple of questions posed in [J. Casas-de la Rosa, S. A. Garcia-Balan, P. J. Szeptycki, \emph{Some star and strongly star selection principles}, Topology Appl. 258 (2019) 572-587]

Keywords

Menger, star Menger, strongly star Menger, Hurewicz, star Hurewicz, strongly star Hurewicz, $\Psi$-spaces, iterated stars.

Supporting Institution

Consejo Nacional de Ciencia y Tecnología (CONACYT, México)

Project Number

Scholarship 769010

Thanks

The first-listed author thanks to Consejo Nacional de Ciencia y Tecnología (CONACYT, México) for the financial support (Scholarship 769010) for this research.

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