Abstract
In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using [2], we "easily" prove that the set strong star Menger and set strong star Hurewicz properties are between countable compactness and the property of having countable extent. Also we show that the extent of a regular set star Menger or a set star Hurewicz space cannot exceed c. Moreover, we construct (1) a consistent example of a set star Menger (set star Hurewicz) space which is not set strongly star Menger (set strongly star Hurewicz) and show that (2) the product of a set star Menger (set star Hurewicz) space with a compact space need not be set star Menger (set star Hurewicz). In particular, (1) and (2) answer some questions posed by Kočinac, Konca and Singh in [17] and [23].
Publisher
Universitat Politecnica de Valencia
Reference26 articles.
1. M. Bonanzinga, F. Cammaroto, and Lj.D.R. Kočinac, Star-Hurewicz and related properties, Applied General Topology 5, no. 1 (2004), 79-89. https://doi.org/10.4995/agt.2004.1996
2. M. Bonanzinga, and F. Maesano, Some properties defined by relative versions of star-covering properties, Topology Appl. 306, no. 1 (2020), 107923. https://doi.org/10.1016/j.topol.2021.107923
3. M. Bonanzinga, and M. V. Matveev, Products of star-Lindelöf and related spaces, Houston Journal of Mathematics 27, no. 1 (2001), 45-57.
4. M. Bonanzinga, and M.V. Matveev, Some covering properties for ψ-spaces, Mat. Vesnik 61 (2009), 3-11.
5. J. Casas-de la Rosa, S. A. Garcia-Balan, and P. J. Szeptycki, Some star and strongly star selection principles, Topolology Appl. 258 (2019), 572-587. https://doi.org/10.1016/j.topol.2017.11.034
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