Some properties defined by relative versions of star-covering properties II

Maddalena Bonanzinga; Davide Giacopello; Fortunato Maesano

doi:10.4995/agt.2023.17926

Authors

Maddalena Bonanzinga University of Messina https://orcid.org/0000-0002-9503-9068
Davide Giacopello University of Messina https://orcid.org/0000-0002-0642-7780
Fortunato Maesano University of Messina https://orcid.org/0000-0003-2580-6230

DOI:

https://doi.org/10.4995/agt.2023.17926

Keywords:

star compact, strongly star compact, star Lindelöf, strongly star Lindelöf, star Menger, strongly star Menger, star Hurewicz, strongly star Hurewicz, set properties

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].

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Author Biographies

Maddalena Bonanzinga, University of Messina

MIFT Department

Davide Giacopello, University of Messina

MIFT Department

Fortunato Maesano, University of Messina

MIFT Department

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