Weaker Forms of Some Star Selection Properties

In this work, we consider weaker forms of some new types of star covering properties, star versions of quasi-Mengerness and related spaces. We discuss the relations of these properties with some other selective covering properties and investigate some topological properties of these spaces.

___

  • [1] L. Babinkostova, B.A. Pansera and M. Scheepers, Weak covering properties and infinite games, Topology Appl. Vol:159 (2012), 3644-3657.
  • [2] L. Babinkostova, B.A. Pansera and M. Scheepers, Weak covering properties and selection principles, Topology Appl. Vol:160 (2013), 2251-2271.
  • [3] P. Daniels, Pixley-Roy spaces over subsets of the reals, Topology Appl. Vol:29 (1988) 93-106.
  • [4] G. Di Maio and Lj.D.R. Koˇcinac, A note on quasi-Menger and similar spaces, Topology Appl. Vol:179 (2015) 148-155
  • [5] R. Engelking, General Topology, Revised and completed ed., Heldermann Verlag, Berlin, 1989.
  • [6] W. Hurewicz, Uber eine Verallgemeinerung des Borelschen Theorems, Math. Zeitschrift Vol:24 (1925), 401-421.
  • [7] W. Hurewicz, Uber Folgen stetiger Funktionen, Fundamenta Math. Vol:9 (1927), 193-204.
  • [8] D. Kocev, Almost Menger and related spaces, Mat. Vesnik Vol:61 (2009) 173-180.
  • [9] D. Kocev, Menger-type covering properties of topological spaces, Filomat Vol:29, No.1 (2015), 99-106. DOI 10.2298/FIL1501099K
  • [10] Lj.D.R. Koˇcinac, Star Menger and related spaces, Publicationes Math. Debr. Vol:55 (1999) 421-431.
  • [11] Lj.D.R. Koˇcinac, Star Menger and related spaces II, Filomat Vol:13 (1999) 129-140.
  • [12] Lj.D.R. Koˇcinac, Addendum to: ”Variations of classical selection principles: an overview”, Quaestiones Math. Vol:37, No.18 (2020), 1121-1153, doi:10.2989/16073606.2019.1601646.
  • [13] Lj.D.R. Koˇcinac and S. Konca, Set-Menger and related properties, Topology Appl. Vol:275 (2020) 106996, doi:10.1016/j.topol.2019.106996.
  • [14] Lj.D.R. Koˇcinac, S. Konca and S. Singh, Set star-Menger and set strongly star-Menger spaces, Math. Slovaca, in press.
  • [15] Lj.D.R. Koˇcinac, S. Konca and S. Singh, Variations of some star selection properties, AIP Conf. Proc., Vol:2334, No.1 (2021).
  • [16] S. Konca and Lj.D.R. Koˇcinac, Set-star Menger and related spaces, Abstract Book VI ICRAPAM 2019 (Istanbul, Turkey, June 12-15, 2019), p.49.
  • [17] K. Menger, Einige Uberdeckungss ¨ atze der Punktmengenlehre, Wien. Ber. Vol:133 (1924) 129-140.
  • [18] B.A. Pansera, Weaker forms of the Menger property, Quaestiones Math. Vol:35 (2012) 161-169.
  • [19] F. Rothberger, Eine Verscharfung der Eigenschaft C, Fundamenta Math. Vol:30 (1938), 50-55.
  • [20] S. Singh, Remarks on set-Menger and related properties, Topology Appl. Vol:280 (2020), Article ID 107278, 4 pages, doi:10.1016/j.topol.2020.107278.