Relative versions of star-Menger property (Q6610431)

Relative topological properties have been studied by various authors. In 1996, \textit{A. V. Arhangel'skii} [Topology Appl. 70, No. 2--3, 87--99 (1996; Zbl 0848.54016)] was interested to initiate a systematic study of this kind of properties and this work has been continued by some other authors.\N\NIn the present paper, the authors introduce and study new relative versions of the star-Menger property related to some properties studied lately by Kočinac, Konca and Singh [\textit{L. D. R. Kočinac} et al., Math. Slovaca 72, No. 1, 185--196 (2022; Zbl 1491.54024)], and Bonanzinga, Giacopello and Maesano [\textit{M. Bonanzinga} et al., Appl. Gen. Topol. 24, No. 2, 391--405 (2023; Zbl 1535.54008)]. In this paper, they provide some examples to understand their relationship with other relativizations of star selection principles. Further, they investigate the behaviour of these spaces under various mappings.