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On almost Hurewicz property in bitopological spaces

Year 2021, Volume: 70 Issue: 1, 74 - 81, 30.06.2021
https://doi.org/10.31801/cfsuasmas.710601

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.

Supporting Institution

University Grants Commision, India

References

  • 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.
Year 2021, Volume: 70 Issue: 1, 74 - 81, 30.06.2021
https://doi.org/10.31801/cfsuasmas.710601

Abstract

References

  • 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.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Harsh Vardhan Chauhan This is me 0000-0002-0888-4221

Beenu Singh 0000-0003-0196-7670

Publication Date June 30, 2021
Submission Date March 28, 2020
Acceptance Date November 25, 2020
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Chauhan, H. V., & Singh, B. (2021). On almost Hurewicz property in bitopological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 74-81. https://doi.org/10.31801/cfsuasmas.710601
AMA Chauhan HV, Singh B. On almost Hurewicz property in bitopological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):74-81. doi:10.31801/cfsuasmas.710601
Chicago Chauhan, Harsh Vardhan, and Beenu Singh. “On Almost Hurewicz Property in Bitopological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 74-81. https://doi.org/10.31801/cfsuasmas.710601.
EndNote Chauhan HV, Singh B (June 1, 2021) On almost Hurewicz property in bitopological spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 74–81.
IEEE H. V. Chauhan and B. Singh, “On almost Hurewicz property in bitopological spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 74–81, 2021, doi: 10.31801/cfsuasmas.710601.
ISNAD Chauhan, Harsh Vardhan - Singh, Beenu. “On Almost Hurewicz Property in Bitopological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 74-81. https://doi.org/10.31801/cfsuasmas.710601.
JAMA Chauhan HV, Singh B. On almost Hurewicz property in bitopological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:74–81.
MLA Chauhan, Harsh Vardhan and Beenu Singh. “On Almost Hurewicz Property in Bitopological Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 74-81, doi:10.31801/cfsuasmas.710601.
Vancouver Chauhan HV, Singh B. On almost Hurewicz property in bitopological spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):74-81.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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