Research Article
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Year 2020, Volume: 49 Issue: 1, 303 - 315, 06.02.2020
https://doi.org/10.15672/hujms.552206

Abstract

References

  • [1] L. Babinkostova, B.A. Pansera and M. Scheepers, Weak covering properties and infinite games, Topol. Appl. 159 3644-3657, 2012.
  • [2] L. Babinkostova, B.A. Pansera and M. Scheepers, Weak covering properties and selection principles, Topol. Appl. 160 (18) 2251-2271, 2013.
  • [3] L.M. Brown, Relations and functions on texture spaces, Preprint.
  • [4] L.M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets Syst. 98 217-224, 1998.
  • [5] L.M. Brown and R. Ertürk, Fuzzy sets as texture spaces, I. Representation theorems, Fuzzy Sets Syst. 110 (2), 227-236, 2000.
  • [6] L.M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology,I. Basic concepts, Fuzzy Sets Syst. 147 (2), 171-199, 2004.
  • [7] L.M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology, II. Topological considerations, Fuzzy Sets Syst. 147 (2), 201-231, 2004.
  • [8] L.M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology, III. Separation Axioms, Fuzzy Sets Syst. 157 (14), 1886-1912, 2006.
  • [9] L.M. Brown and M.M. Gohar, Compactness in ditopological texture spaces, Hacet. J. Math. Stat. 38 21-43, 2009.
  • [10] G. Di Maio and Lj. D.R. Kočinac, Some covering properties of hyperspaces, Topol. Appl. 155 1959-1969, 2008.
  • [11] Ş. Dost, Semi-open and semi-closed sets in ditopological texture spaces, J. Adv. Math. Stud. 5 (1), 97-110, 2012.
  • [12] M.M. Gohar, Compactness in ditopological texture spaces, PhD Thesis Hacettepe University, Turkey 2002.
  • [13] D. Kocev, Almost Menger and related spaces, Mat. Vesn. 61 173-180, 2009.
  • [14] Lj. D.R. Kočinac, Star-Menger and related spaces II, Filomat 13 129-140, 1999.
  • [15] Lj. D.R. Kočinac, The PixleyRoy topology and selection principles, Quest. Answers Gen. Topology 19 219-225, 2001.
  • [16] Lj. D.R. Kočinac, Selected results on selection principles, In: Proceedings of the 3rd Seminar on Geometry and Topology (Sh. Rezapour, ed.), July 71-104, 2004.
  • [17] Lj. D.R. Kočinac, A note on mappings and almost Menger and related spaces, University Thought: Publications in Natural Sciences 6 (1), 67-70, 2016.
  • [18] Lj. D.R. Kočinac and S. Özçağ, Selection properties of texture structures, Topol. Appl. 192 158-168, 2015.
  • [19] Lj. D.R. Kočinac and S. Özçağ, Hurewicz-type properties in texture structures, Topol. Appl. 221 286-299, 2017.
  • [20] M. Kule and Ş. Dost, Ditopological texture spaces and semi-regularity axioms, Ann. Fuzzy Math. Inform. 12 (1), 47-62, 2016.
  • [21] N. Levine, Semi-open sets and semi-continuity in topological spaces, Am. Math. Mon 70 (1), 36-41, 1963.
  • [22] B.A. Pansera, Weaker forms of the Menger property, Quaest. Math. 35 161-169, 2012.
  • [23] A. Sabah, M. Khan and Lj. D.R. Kočinac, Covering properties defined by semi-open sets, J. Nonlinear Sci. Appl. 9 4388-4398, 2016.
  • [24] M. Sakai, The weak Hurewicz property of Pixley-Roy hyperspaces, Topol. Appl. 160 2531-2537, 2012.
  • [25] O. A. E. Tantawy, S. A. El-Sheikh, M. Yakout and M.A. Latif, On connectedness in ditopological texture spaces, Ann. Fuzzy Math. Inform. 343-354 2014.
  • [26] H. Ullah and M. Khan, Almost-Menger, Rothberger and Hurewicz type properties in ditopological texture spaces, Submitted.

Almost-s-Menger ditopological texture spaces

Year 2020, Volume: 49 Issue: 1, 303 - 315, 06.02.2020
https://doi.org/10.15672/hujms.552206

Abstract

The aim of this article is to introduce and characterize almost-s-Menger and almost-co-s-Menger selection properties in ditopological texture spaces. We prove that every s-Menger ditopological texture space is almost-s-Menger and every s-compact ditopological texture space is almost-s-Menger, and give an example which shows that the converse is not true in general.

References

  • [1] L. Babinkostova, B.A. Pansera and M. Scheepers, Weak covering properties and infinite games, Topol. Appl. 159 3644-3657, 2012.
  • [2] L. Babinkostova, B.A. Pansera and M. Scheepers, Weak covering properties and selection principles, Topol. Appl. 160 (18) 2251-2271, 2013.
  • [3] L.M. Brown, Relations and functions on texture spaces, Preprint.
  • [4] L.M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets Syst. 98 217-224, 1998.
  • [5] L.M. Brown and R. Ertürk, Fuzzy sets as texture spaces, I. Representation theorems, Fuzzy Sets Syst. 110 (2), 227-236, 2000.
  • [6] L.M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology,I. Basic concepts, Fuzzy Sets Syst. 147 (2), 171-199, 2004.
  • [7] L.M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology, II. Topological considerations, Fuzzy Sets Syst. 147 (2), 201-231, 2004.
  • [8] L.M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology, III. Separation Axioms, Fuzzy Sets Syst. 157 (14), 1886-1912, 2006.
  • [9] L.M. Brown and M.M. Gohar, Compactness in ditopological texture spaces, Hacet. J. Math. Stat. 38 21-43, 2009.
  • [10] G. Di Maio and Lj. D.R. Kočinac, Some covering properties of hyperspaces, Topol. Appl. 155 1959-1969, 2008.
  • [11] Ş. Dost, Semi-open and semi-closed sets in ditopological texture spaces, J. Adv. Math. Stud. 5 (1), 97-110, 2012.
  • [12] M.M. Gohar, Compactness in ditopological texture spaces, PhD Thesis Hacettepe University, Turkey 2002.
  • [13] D. Kocev, Almost Menger and related spaces, Mat. Vesn. 61 173-180, 2009.
  • [14] Lj. D.R. Kočinac, Star-Menger and related spaces II, Filomat 13 129-140, 1999.
  • [15] Lj. D.R. Kočinac, The PixleyRoy topology and selection principles, Quest. Answers Gen. Topology 19 219-225, 2001.
  • [16] Lj. D.R. Kočinac, Selected results on selection principles, In: Proceedings of the 3rd Seminar on Geometry and Topology (Sh. Rezapour, ed.), July 71-104, 2004.
  • [17] Lj. D.R. Kočinac, A note on mappings and almost Menger and related spaces, University Thought: Publications in Natural Sciences 6 (1), 67-70, 2016.
  • [18] Lj. D.R. Kočinac and S. Özçağ, Selection properties of texture structures, Topol. Appl. 192 158-168, 2015.
  • [19] Lj. D.R. Kočinac and S. Özçağ, Hurewicz-type properties in texture structures, Topol. Appl. 221 286-299, 2017.
  • [20] M. Kule and Ş. Dost, Ditopological texture spaces and semi-regularity axioms, Ann. Fuzzy Math. Inform. 12 (1), 47-62, 2016.
  • [21] N. Levine, Semi-open sets and semi-continuity in topological spaces, Am. Math. Mon 70 (1), 36-41, 1963.
  • [22] B.A. Pansera, Weaker forms of the Menger property, Quaest. Math. 35 161-169, 2012.
  • [23] A. Sabah, M. Khan and Lj. D.R. Kočinac, Covering properties defined by semi-open sets, J. Nonlinear Sci. Appl. 9 4388-4398, 2016.
  • [24] M. Sakai, The weak Hurewicz property of Pixley-Roy hyperspaces, Topol. Appl. 160 2531-2537, 2012.
  • [25] O. A. E. Tantawy, S. A. El-Sheikh, M. Yakout and M.A. Latif, On connectedness in ditopological texture spaces, Ann. Fuzzy Math. Inform. 343-354 2014.
  • [26] H. Ullah and M. Khan, Almost-Menger, Rothberger and Hurewicz type properties in ditopological texture spaces, Submitted.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Hafiz Ullah 0000-0002-6600-8852

Moiz Ud Din Khan

Publication Date February 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 1

Cite

APA Ullah, H., & Khan, M. U. D. (2020). Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics, 49(1), 303-315. https://doi.org/10.15672/hujms.552206
AMA Ullah H, Khan MUD. Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics. February 2020;49(1):303-315. doi:10.15672/hujms.552206
Chicago Ullah, Hafiz, and Moiz Ud Din Khan. “Almost-S-Menger Ditopological Texture Spaces”. Hacettepe Journal of Mathematics and Statistics 49, no. 1 (February 2020): 303-15. https://doi.org/10.15672/hujms.552206.
EndNote Ullah H, Khan MUD (February 1, 2020) Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics 49 1 303–315.
IEEE H. Ullah and M. U. D. Khan, “Almost-s-Menger ditopological texture spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, pp. 303–315, 2020, doi: 10.15672/hujms.552206.
ISNAD Ullah, Hafiz - Khan, Moiz Ud Din. “Almost-S-Menger Ditopological Texture Spaces”. Hacettepe Journal of Mathematics and Statistics 49/1 (February 2020), 303-315. https://doi.org/10.15672/hujms.552206.
JAMA Ullah H, Khan MUD. Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics. 2020;49:303–315.
MLA Ullah, Hafiz and Moiz Ud Din Khan. “Almost-S-Menger Ditopological Texture Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, 2020, pp. 303-15, doi:10.15672/hujms.552206.
Vancouver Ullah H, Khan MUD. Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):303-15.