Year 2020,
Volume: 49 Issue: 1, 303 - 315, 06.02.2020
Hafiz Ullah
,
Moiz Ud Din Khan
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
Hafiz Ullah
,
Moiz Ud Din Khan
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.