On almost Hurewicz property in bitopological spaces

The purpose of this paper is to investigate properties and results of the almost Hurewicz property in bitopological spaces. We characterize this property using $(i, j)$- regular open sets and almost continuous surjective map.

___

  • Datta, M.C., Projective bitopological spaces II, J. Aust. Math. Soc., 14 (1972), 119-128.
  • Dvalishvili, B.P., Bitopological spaces: Theory, relations with generalized algebraic structures and applications, North Holland Mathematics studiesm, Elsevier science B.V., Amsterdam, (2005).
  • Engelking, R., General Topology, Heldermann Verlag, Berlin, (1989).
  • Eysen, A., Özça¼g, S., Weaker forms of the Menger property in bitopological spaces, Quaest. Math., 41(7) (2018), 877-888.
  • Hurewicz, W., Über die verallgemeinerung des Borelschen Theorems, Math. Z., 24 (1925), 401-425.
  • Hurewicz, W., Über Folgen Stetiger Funktionen, Fund. Math., 9 (1927), 193-204.
  • Jeli´c, M., Feebly p-continuous mappings, V International meeting on topology in Italy (Ital- ian) (Lecce,1990/Otranto, 1990); Rend. Circ. Mat. Palermo, 24 (2) (1990), 387-395.
  • Khan, M.D., Sabah, A., Selection principles and covering properties in bitopological spaces, Applied General Topology, 21(1) (2020), 159 -169.
  • Khedr, F.H., Alshibani, A.M., On pairwise super continuous mappings in bitopological spaces, Int. J. Math. Math. Sci., 14(4) (1991), 715- 722.
  • Koµcinac, Lj.D.R., The Pixley-Roy topology and selection principles, Questions and Answers in General Topology, 19(2) (2001), 219-225.
  • Koµcinac, Lj.D.R., The Reznichenko property and the Pytkeev property in hyperspaces, Acta Mathematica Hungarica, 107(3) (2005), 225-233
  • Koµcinac, Lj.D.R., Özça¼g, S., Versions of separability in bitopological spaces, Topology and its Applications 158 (2011), 1471-1477.
  • Koµcinac, Lj.D.R., Özça¼g, S., Bitopological spaces and selection principles, Proceedings ICTA 2011, Cambridge Scienti…c Publishers, (2012), 243- 255.
  • Lyakhovets, D., Osipov, A.V., Selection principles and games in bitopological function spaces, Filomat, 33(14) (2019), 4535- 4540.
  • Maheshwari, S.N., Prasad, R. Semi open sets and semi continuous function in bitopological spaces, Math. Notes 26 (1977 -78), 29 -37.
  • Menger, K., Einige Überdeckungssätze der Punktmengenlehre, Sitzungsber. Österr. Adad. Wiss. Math.-Naturwiss. Kl. Abt IIa, 133 (1924), 421- 444.
  • Özçağ, S., Bornologies and bitopological function spaces, Filomat 27(7) (2013), 1345-1349.
  • Özçağ, S., Selective bitopological version of separability, Topology and its Applications, 201 (2016), 403-413.
  • Özçağ, S., Eysen, A.E., Almost Menger property in bitopological spaces, Ukrainian Math. J., 68(6) (2016), 950 -958.
  • Rothberger, F., Eine Verscharfung der Eigenschaft C, Fund. Math. 30 (1938), 50- 55.
  • Sakai, M., The weak Hurewicz property of Pixley-Roy hyperspaces, Topology and its Appli- cations, 160(18) (2013), 2531- 2537.
  • Scheepers, M., Combinatorics of open covers I: Ramsey theory, Topology Appl. 69 (1996), 31 -62.
  • Singal, A.R., Arya, S.P., On pairwise almost regular spaces, Glasnik Math. 26(6) (1971), 335 -343.
  • Song, Y.K., Li, R., The almost Hurewicz spaces, Questions and Answers in General Topology 31 (2013), 131- 136.
  • Song, Y.K., Li, R., On weakly Hurewicz spaces, Filomat 29(4) (2015), 667-671.