On topological soft sets

Kandemir, M. Burç; Tanay, B.

doi:10.2478/jamsi-2020-0006

Abstract

In this paper, we have established topological soft sets over generalized topological spaces and topological spaces, and studied its structural properties. We have derived a topological soft set in any given topological space, and from this point of view, we have given necessary and sufficient condition for homeomorphic Alexandroff spaces using topological soft set technique. At last, we have derived a topological soft set using closed sets in any topological space and we have given necessary and sufficient condition for arbitrary homeomorphic topological spaces using them.

References

Abd El-Monsef M. E., El-Deeb S. N., Mahmoud R. A., β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
Search in Google Scholar Back to article
Aktaş H., Çağman N., Soft sets and soft groups, Inform. Sciences. 177 (2007) 2726–2735.
Search in Google Scholar Back to article
Alexandroff P., Diskrete Räume, Rec. Math. [Mat. Sbornik] N.S. Vol. 2 (44) (1937), 501–519.
Search in Google Scholar Back to article
Ali M. I., Feng F., Liu X. Y., Min W. K., Shabir M., On Some New Operations in Soft Set Theory, Comput. Math. Appl. 57 (2009) 1547-1553.
Search in Google Scholar Back to article
Császár Á., Generalized open sets, Acta Math. Hungar. 75 (1997), 65–87.
Search in Google Scholar Back to article
Császár Á., Generalized topology, generalized continuity, Acta Math. Hungar. 96 (4) (2002), 351–357.
Search in Google Scholar Back to article
Császár Á., Generalized open sets in generalized topology, Acta Math. Hungar. 106 (2005), 53–66.
Search in Google Scholar Back to article
Ge X., Li Z., Ge Y., Topological spaces and soft sets, J. Comput. Anal. Appl. 13 (4) (2011) 881–885.
Search in Google Scholar Back to article
Kharal A., Ahmad B., Mappings on soft classes, New Math. and Nat. Computation 7 (3) (2011) 471–481.
Search in Google Scholar Back to article
Levine N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41.
Search in Google Scholar Back to article
Li Z., Chen H., Gao N., The topological structure on soft sets, J. Comput. Anal. Appl. 15 (4) (2013) 746–752.
Search in Google Scholar Back to article
Maji P. K., Biswas R., Roy A. R., Soft set theory, Comput. Math. Appl. 45 (2003) 555-562.
Search in Google Scholar Back to article
Mashhour A. S., Abd El-Monsef M. E., El-Deeb S. N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
Search in Google Scholar Back to article
Min W. K., Similarity in soft set theory, Appl. Math. Lett. 25 (2012) 310–314.
Search in Google Scholar Back to article
Min W. K., Soft sets over a common topological universe, Journal of Intelligent & Fuzzy Systems, vol. 26 (5) (2014) 2099-2106.
Search in Google Scholar Back to article
Molodtsov D., Soft sets-first results, Comput. Math. Appl. 37 (1999) 19–31.
Search in Google Scholar Back to article
Njåstad O., On some classes of nearly open sets, Pasific J. Math. 15 (1965), 961–970.
Search in Google Scholar Back to article
Pei D., Miao D., From Soft Sets to Information Systems, Proceedings of IEEE International Conference on Granular Computing 2 (2005) 617-621.
Search in Google Scholar Back to article
Qin K., Hong Z., On soft equality, J. Comput. Appl. Math. 234 (2010) 1347–1355.
Search in Google Scholar Back to article
Shabir M., Naz M., On soft topological spaces, Comput. Math. Appl. 61 (2011) 1786–1799.
Search in Google Scholar Back to article

On topological soft sets

Abstract

Paradigm

My account