拓扑空间上星形选择特性的迭代与联合

Pub Date : 2024-04-14 DOI:10.15672/hujms.1198061

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

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引用次数: 0

摘要

在本文中，我们研究了具有某些（星形）选择原则的空间的小（关于边界数和支配数）联盟具有哪些选择原则性质。此外，我们还给出了这些性质的迭代结果以及比共容性更弱的性质。此外，我们还研究了这些迭代性质在 $\Psi$ 空间上的行为。最后，我们证明了有一个正常的星-门格尔空间不是强星-门格尔空间；这个例子回答了[J.Casas-de la Rosa, S. A. Garcia-Balan, P. J. Szeptycki, \emph{一些星形和强星形选择原则}, Topology Appl.

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Iterations and unions of star selection properties on topological spaces

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]

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