On almost Hurewicz property in bitopological spaces

Abstract

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.

Keywords

• Hurewicz property
• almost Hurewicz property
• Bitopological space
• Menger property

References

1. Datta, M.C., Projective bitopological spaces II, J. Aust. Math. Soc., 14 (1972), 119-128.
2. Dvalishvili, B.P., Bitopological spaces: Theory, relations with generalized algebraic structures and applications, North Holland Mathematics studiesm, Elsevier science B.V., Amsterdam, (2005).
3. Engelking, R., General Topology, Heldermann Verlag, Berlin, (1989).
4. Eysen, A., Özça¼g, S., Weaker forms of the Menger property in bitopological spaces, Quaest. Math., 41(7) (2018), 877-888.
5. Hurewicz, W., Über die verallgemeinerung des Borelschen Theorems, Math. Z., 24 (1925), 401-425.
6. Hurewicz, W., Über Folgen Stetiger Funktionen, Fund. Math., 9 (1927), 193-204.
7. 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.
8. Khan, M.D., Sabah, A., Selection principles and covering properties in bitopological spaces, Applied General Topology, 21(1) (2020), 159 -169.

9. Khedr, F.H., Alshibani, A.M., On pairwise super continuous mappings in bitopological spaces, Int. J. Math. Math. Sci., 14(4) (1991), 715- 722.
10. Koµcinac, Lj.D.R., The Pixley-Roy topology and selection principles, Questions and Answers in General Topology, 19(2) (2001), 219-225.
11. Koµcinac, Lj.D.R., The Reznichenko property and the Pytkeev property in hyperspaces, Acta Mathematica Hungarica, 107(3) (2005), 225-233
12. Koµcinac, Lj.D.R., Özça¼g, S., Versions of separability in bitopological spaces, Topology and its Applications 158 (2011), 1471-1477.
13. Koµcinac, Lj.D.R., Özça¼g, S., Bitopological spaces and selection principles, Proceedings ICTA 2011, Cambridge Scienti…c Publishers, (2012), 243- 255.
14. Lyakhovets, D., Osipov, A.V., Selection principles and games in bitopological function spaces, Filomat, 33(14) (2019), 4535- 4540.
15. Maheshwari, S.N., Prasad, R. Semi open sets and semi continuous function in bitopological spaces, Math. Notes 26 (1977 -78), 29 -37.
16. Menger, K., Einige Überdeckungssätze der Punktmengenlehre, Sitzungsber. Österr. Adad. Wiss. Math.-Naturwiss. Kl. Abt IIa, 133 (1924), 421- 444.
17. Özçağ, S., Bornologies and bitopological function spaces, Filomat 27(7) (2013), 1345-1349.
18. Özçağ, S., Selective bitopological version of separability, Topology and its Applications, 201 (2016), 403-413.
19. Özçağ, S., Eysen, A.E., Almost Menger property in bitopological spaces, Ukrainian Math. J., 68(6) (2016), 950 -958.
20. Rothberger, F., Eine Verscharfung der Eigenschaft C, Fund. Math. 30 (1938), 50- 55.
21. Sakai, M., The weak Hurewicz property of Pixley-Roy hyperspaces, Topology and its Appli- cations, 160(18) (2013), 2531- 2537.
22. Scheepers, M., Combinatorics of open covers I: Ramsey theory, Topology Appl. 69 (1996), 31 -62.
23. Singal, A.R., Arya, S.P., On pairwise almost regular spaces, Glasnik Math. 26(6) (1971), 335 -343.
24. Song, Y.K., Li, R., The almost Hurewicz spaces, Questions and Answers in General Topology 31 (2013), 131- 136.
25. Song, Y.K., Li, R., On weakly Hurewicz spaces, Filomat 29(4) (2015), 667-671.