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β-SELECTION PROPERTIES IN DITOPOLOGICAL TEXTURE SPACES

Year 2020, Volume: 38 Issue: 2, 1019 - 1029, 01.06.2021

Abstract

In the present paper, we continue previous investigations on the selection properties in ditopological texture spaces. We introduce the β-Menger and β-Rothberger properties and examine some their properties in ditopological texture spaces. The subject of our investigation is also the preservation of β-Menger property under subspaces, products, and -continuous mappings.

References

  • [1] M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci., Assiut Univ. 12 (1983), 77-90.
  • [2] T. Aho and T. Nieminen, Spaces in which preopen subsets are semiopen, Ricerche di Matematica 43 (1) (1994), 45-59.
  • [3] D. Andrijević, Semi-preopen sets, Mat. Vesnik 38 (1986), 24-32.
  • [4] Aqsa and M. ud Din Khan, On nearly Menger and nearly star Menger spaces, Filomat 33 (2019), 6219-6227.
  • [5] L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems, 98 (1998) 217–224.
  • [6] L.M. Brown and R. Ertürk, Fuzzy Sets as Texture Spaces, I. Representation Theorems, Fuzzy Sets and Systems, 110(2)(2000), 227-236.
  • [7] L.M. Brown and R. Ertürk, Fuzzy sets as texture spaces, II. Subtextures and quotient textures, Fuzzy Sets and Systems 110(2)(2000), 237-245.
  • [8] L. M. Brown, R. Ertürk and Ş. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147, No. 2 (2004) 171–199.
  • [9] M. Caldas and S. Jafari, A new decomposition of β-open functions, Chaos Solitons & Fractals 40 (2009), 10-12.
  • [10] M. Diker, Textural approach to rough sets based on relations, Inf. Sci. 180, No. 8 (2010) 1418–1433 .
  • [11] Ş. Dost, A textural view of soft fuzzy rough sets, J. Intell. Fuzzy Syst. 28 (2015), 2519-2535.
  • [12] Ş. Dost, L. M. Brown and R. Ertürk, β-open and β-closed sets in ditopological setting, Filomat 481:24 (2) (2010) 11–26.
  • [13] M. Ganster and D. Andrijevic, On some questions concerning semi-preopen sets, J. Inst. Math. & Comp. Sci. (Math. Ser.) 1 (2) (1988), 65-75.
  • [14] Lj. D. R. Koc ̆inac, Variations of classical selection principles: An overview, Quaest. Math., (2019), in press (Doi: 10.2989/16073606.2019.1601646).
  • [15] Lj. D. R. Koc ̆inac, Generalized open sets and selection properties, Filomat 33 (2019), 1485-1493.
  • [16] Lj. D. R. Koc ̆inac and S. Özçağ, Selection properties of texture structures, Topol. Appl. 192 (2015), 158-168.
  • [17] Lj. D. R. Koc ̆inac and S. Özçağ, Hurewicz-type properties in texture structures, Topol. Appl. 221 (2017), 286-299.
  • [18] M. Kule and Ş. Dost, A textural view of semi-separation axioms in soft fuzzy topological spaces, J. Intell. Fuzzy Syst. 30 (2016) 2037-2053.
  • [19] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.
  • [20] A. S. Mashour, M. E. Abd El-Monsef and El-Deeb., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.
  • [21] K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik (Wiener Akademie, Wien) 133 (1924), 421-444.
  • [22] F. Rothberger, Eine Verschärfung der Eigenschaft C, Fund. Math. 30 (1938), 50–55.
  • [23] H. Ullah and M. ud Din Khan, Almost-s-Menger ditopological texture spaces, Hacet. J. Math. Stat., 49:1 (2020), 303–315.
  • [24] H. Ullah and M. ud Din Khan, Semi-Hurewicz-Type properties in ditopological texture spaces, Open Mathematics, 16 (2018), 1243-1254.
  • [25] H. Ullah and M. ud Din Khan, Almost-s-Hurewicz ditopological texture spaces, Ann. Fuzzy Math. Inform. 19:2 (2020), 199-209.
  • [26] A. Sabah, M. ud Din Khan and Lj. D. R. Koc ̆inac, Covering properties defined by semi-open sets, J. Nonlinear Sci. Appl. 9 (2016), 4388-4398.
  • [27] S. Todorc ̆ević, Aronszajn orderings, Publ. Inst. Math. 57 (1995), 29–46.
There are 27 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Memet Kule This is me 0000-0002-2869-2358

Şenol Dost This is me

Publication Date June 1, 2021
Submission Date January 15, 2020
Published in Issue Year 2020 Volume: 38 Issue: 2

Cite

Vancouver Kule M, Dost Ş. β-SELECTION PROPERTIES IN DITOPOLOGICAL TEXTURE SPACES. SIGMA. 2021;38(2):1019-2.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/