@article{article_1198061, title={Iterations and unions of star selection properties on topological spaces}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={54}, pages={180–199}, year={2025}, DOI={10.15672/hujms.1198061}, author={Casas-de La Rosa, Javier and Chen-mertens, William and Garcia-balan, Sergio A.}, keywords={Menger, star-Menger, strongly star-Menger, Hurewicz, star-Hurewicz, strongly star-Hurewicz, star selection principles, -spaces, iterated stars}, 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, Some star and strongly star selection principles, Topology Appl. 258, 572-587, 2019].}, number={1}, publisher={Hacettepe University}, organization={Consejo Nacional de Ciencia y Tecnología (CONACYT, México)}