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 Research Article
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 1.Ullah H, Khan MUD. Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):303-315. doi:10.15672/hujms.552206
Chicago Ullah, Hafiz, and Moiz Ud Din Khan. 2020. “Almost-S-Menger Ditopological Texture Spaces”. Hacettepe Journal of Mathematics and Statistics 49 (1): 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 [1]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, Feb. 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 1, 2020): 303-315. https://doi.org/10.15672/hujms.552206.
JAMA 1.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, Feb. 2020, pp. 303-15, doi:10.15672/hujms.552206.
Vancouver 1.Ullah H, Khan MUD. Almost-s-Menger ditopological texture spaces. Hacettepe Journal of Mathematics and Statistics [Internet]. 2020 Feb. 1;49(1):303-15. Available from: https://izlik.org/JA65KZ52KK