Some observations on Hurewicz and \(\mathcal{I}\)-Hurewicz property
In this paper the authors study some observations on the Hurewicz and the $\mathcal{I}$-Hurewicz property. We know that the ideal variant of the Hurewicz property, the $\mathcal{I}$-Hurewicz property was introduced and studied by \textit{P. Das} [Houston J. Math. 39, No. 2, 637--650 (2013; Zbl 1273.54022)] (later in [\textit{P. Das} et al., Topology Appl. 202, 183--193 (2016; Zbl 1337.54010)]). The $\mathcal{I}$-Hurewicz property defined here is the $\mathcal{F}$-Menger property [\textit{T. Banakh} et al., Topology Appl. 157, No. 2, 466--481 (2010; Zbl 1184.54033)] and a more general version called $\mathcal{S}$-Menger property has been recently studied in [\textit{P. Szewczak} and \textit{B. Tsaban}, Ann. Pure Appl. Logic 168, No. 1, 1--18 (2017; Zbl 1355.54026)]. In Sections 3.1, 3.2, 3.3 and 3.4, the authors give interesting results concering the Hurewicz and the $\mathcal{I}$-Hurewicz property using selection principles and preservation of the $\mathcal{I}$-Hurewicz property. Finally, in Section 3.5 they present observations on the $\mathcal{I}$-Hurewicz property in certain special structures.
scientific article; zbMATH DE number 7047518
scientific article