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Selection principles in the context of soft sets: Menger spaces

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Abstract

The aim of this paper is to consider the Menger selection principle in the context of soft sets and to discuss its several features in this context. From this point of view, we first propose some new soft open covers and investigate their relations. We extend two well-known covering properties called Rothberger and Menger selection properties, appropriately to the soft setting. Then, we concentrate on soft Menger spaces and discuss most of the important properties of these soft topological spaces such as relations with its parameter topological spaces, subspaces, behavior under soft mappings, product spaces, and so on.

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References

  • Açıkgöz A, Taş N (2016) Binary soft set theory. Eur J Pure Appl Math 9(4):452–463

    MathSciNet  MATH  Google Scholar 

  • Ali MI, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Computers Math Appl 57(9):1547–1553

    Article  MathSciNet  MATH  Google Scholar 

  • Al-shami TM (2019) Comments on “Soft mappings spaces’’. Scientif World J 45:2

    Google Scholar 

  • Al-shami TM (2020) Comments on some results related to soft separation axioms. Afrika Matematika 31(7):1105–1119

    Article  MathSciNet  MATH  Google Scholar 

  • Al-shami TM (2021) Compactness on soft topological ordered spaces and its application on the information system. J Math 6699092:12

    MathSciNet  MATH  Google Scholar 

  • Al-shami TM (2021) On soft separation axioms and their applications on decision-making problem. Math Probl Eng 8876978: 12

  • Al-shami TM, El-Shafei ME (2020) Partial belong relation on soft separation axioms and decision making problem: two birds with one stone. Soft Comput 24(7):5377–5387

    Article  Google Scholar 

  • Al-shami TM, El-Shafei ME, Abo-Elhamayel M (2018) Almost soft compact and approximately soft Lindelöf spaces. J Taibah Univ Sci 12(5):620–630

    Article  Google Scholar 

  • Alshami TM, Kočinac LJDR (2019) The equivalence between the enriched and extended soft topologies. Appl Comput Math 18(2):149–162

    MathSciNet  MATH  Google Scholar 

  • Al-shami TM, Kočinac LJDR, Asaad BA (2020) Sum of soft topological spaces. Mathematics 8(6):990

    Article  Google Scholar 

  • Aygünoǧlu A, Aygün H (2012) Some notes on soft topological spaces. Neural Comput Appl 21(1):113–119

    Article  Google Scholar 

  • Babitha KV, Suntil JJ (2010) Soft set relations and functions. Computers Math Appl 60(7):1840–1849

    Article  MathSciNet  MATH  Google Scholar 

  • Çağman N, Karataş S, Enginoglu S (2011) Soft topology. Computers Math Appl 62:351–358

    Article  MathSciNet  MATH  Google Scholar 

  • Çetkin V, Aygünoǧlu A, Aygün H (2016) CATS of soft topological spaces. J Intell Fuzzy Syst 30(4):1903–1913

    Article  MATH  Google Scholar 

  • Das S, Samanta SK (2013) Soft metric. Annals Fuzzy Math Inform 6(1):77–94

    MathSciNet  MATH  Google Scholar 

  • El-Shafei ME, Abo-Elhamayel M, Al-shami TM (2018) Partial soft separation axioms and soft compact spaces. Filomat 32(13):4755–4771

    Article  MathSciNet  Google Scholar 

  • ElShafei ME, Alshami TM (2020) Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem. Comp Appl Math 39:138 (2020). https://doi.org/10.1007/s40314-020-01161-3

  • Engelking R (1989) General topology. Heldermann-Verlag, Berlin

    MATH  Google Scholar 

  • Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2018) N-soft sets and their decision making algorithms. Soft Comput 22:3829–3842

    Article  MATH  Google Scholar 

  • Feng F, Li YM, Davvaz B, Ali MI (2010) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911

    Article  MATH  Google Scholar 

  • Hida T (2014) A comprasion of two formulations of soft compactness. Ann Fuzzy Math Inf 8(4):511-524

    MATH  Google Scholar 

  • Hurewicz W (1925) Über ein Verallgemeinerung des Borelschen Theorems. Math Zeitschrift 24:401–425 ((in German))

    Article  MATH  Google Scholar 

  • Hurewicz W (1927) Über Folgen stetiger Funktionen. Fundamenta Mathematicae 9:193–204 ((in German))

    Article  MATH  Google Scholar 

  • Jun YB, Ahn SS (2019) Double-Framed soft sets with applications in BCK/BCI-Algebras. J Appl Math 178159:15

    MATH  Google Scholar 

  • Just W, Miller AW, Scheepers M, Szeptycki PJ (1996) The combinatorics of open covers (II). Topol Appl 73(3):241–266

    Article  MathSciNet  MATH  Google Scholar 

  • Kharal A, Ahmad B (2011) Mappings on soft classes. New Math Nat Comput 7(3):471–481

    Article  MathSciNet  MATH  Google Scholar 

  • Kočinac LjDR. Selected results on selection principles, in: Proc. Third Seminar Geom. Topol, Tabriz, Iran, July 15–17, (2004) pp. 71–104

  • Kočinac LjDR (2015) Star selection principles: a survey. Khayyam J Math 1(1):82–106

    MathSciNet  MATH  Google Scholar 

  • Kočinac LjDR (2019) Generalized open sets and selection properties. Filomat 33(5):1485–1493

    Article  MathSciNet  Google Scholar 

  • Kočinac LjDR (2020) Variations of classical selection principles: an overview. Quaest. Math. 37(8):1121–1153

    Article  MathSciNet  MATH  Google Scholar 

  • Kočinac LjDR, Scheepers M (2003) Combinatorics of open covers (VII): Groupability. Fund. Math. 179(2):131–155

    Article  MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy R (2001) Fuzzy soft sets. J Fuzzy Math 9:589–602

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy R (2003) Soft set theory. Computers Math Appl 45(4–5):555–562

    Article  MathSciNet  MATH  Google Scholar 

  • Matejdes M (2021) Methodological remarks on soft topology. Soft Comput 25(11):1–8

    Google Scholar 

  • Menger K. Einige Überdeckungssätze der Punktmengenlehre. Stzungsberischte Abt. 3a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik 1924; 133: 421–444 (in German)

  • Molodtsov D (1999) Soft set theory-first results. Computers Math Appl 37(4–5):19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Nazmul S, Samanta SK (2013) Neighbourhood properties of soft topological spaces. Ann Fuzzy Math Inf 6(1):1–15

  • Rothberger F (1938) Eine Verschärfung der Eigenschaft C. Fundamenta Mathematicae 30:50–55 ((in German))

    Article  MATH  Google Scholar 

  • Sakai M, Scheepers M (2014) The combinatorics of open covers. In: Hart KP, van Mill J, Simon P (eds) Recent progress in general topology III. Atlantis Press, Paris

    Google Scholar 

  • Scheepers M (1996) Combinatorics of open covers (I): Ramsey theory. Topol Appl 69(1):31–62

    Article  MathSciNet  MATH  Google Scholar 

  • Shabir M, Gul R (2020) Modified rough bipolar soft sets. J Intell Fuzzy Syst 39(3):4259–4283

    Article  Google Scholar 

  • Shabir M, Naz M (2011) On soft topological spaces. Computers Math Appl 61(7):1786–1799

    Article  MathSciNet  MATH  Google Scholar 

  • Shabir M, Naz M (2013) On bipolar soft sets. http://arxiv.org/abs/1303.1344v1

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Acknowledgements

The author would like to thank the referees for their valuable comments, which helped us to improve the manuscript.

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Authors and Affiliations

  1. University of Niš, Faculty of Sciences and Mathematics, Niš, Serbia

    Ljubiša D. R. Kočinac

  2. Department of Mathematics, Sana’a University, Sana’a, Yemen

    Tareq M. Al-shami

  3. Department of Mathematics, Kocaeli University, Kocaeli, Turkey

    Vildan Çetkin

Authors
  1. Ljubiša D. R. Kočinac
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  2. Tareq M. Al-shami
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  3. Vildan Çetkin
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Correspondence to Tareq M. Al-shami.

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Kočinac, L.D.R., Al-shami, T.M. & Çetkin, V. Selection principles in the context of soft sets: Menger spaces. Soft Comput 25, 12693–12702 (2021). https://doi.org/10.1007/s00500-021-06069-6

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