More notions and mappings via somewhere dense sets
Tóm tắt
In this paper, the authors continue studying more properties of somewhere dense sets. They derive some interesting results related to them such as the collection of all somewhere dense subsets of a strongly hyperconnected space
$$(X,\tau )$$
forms a filter on X, and a topological space which contains at least two disjoint somewhere dense sets is an
$$ST_1$$
-space. Then they introduce and study a concept of S-limit points of a soft set. Depending on somewhere dense and cs-dense sets, they also define and investigate various maps between topological spaces, namely SD-continuous, SD-irresolute, SD-open, SD-closed and SD-homeomorphism maps.
Tài liệu tham khảo
Abd El-Monsef, M.E., Kozae, A.M., Iqelan, M.J.: Near approximations in topological spaces. Int. J. Math. Anal. (Ruse) 4(6), 279–290 (2010)
Abd El-Monsef, M.E., El-Deeb, S.N., Mahmoud, R.A.: \(\beta \)-open sets and \(\beta \)-continuous mappings. Bull. Fac. Sci. Assiut Univ. 12, 77–90 (1983)
Akdag, M., Ozkan, A.: Soft \(\alpha \)-open sets and soft \(\alpha \)-continuous functions. Abstr. Appl. Anal. 1–7 (2014) (Art ID 891341)
Akdag, M., Ozkan, A.: Soft \(b\)-open sets and soft \(b\)-continuous functions. Math. Sci. (Springer) 8, 1–9 (2014)
Alpers, A.: Digital topology: regular sets and root images of the cross median filter. J. Math. Imaging Vis. 17, 7–14 (2002)
Al-shami, T.M.: Somewhere dense sets and \(ST_1\)-spaces. Punjab Univ. J. Math. (Lahore) 49(2), 101–111 (2017)
Al-shami, T.M.: Soft somewhere dense sets on on soft topological spaces. Commun. Korean Math. Soc. 33(4), 1341–1356 (2018)
Andrijevic̀, D.: On \(b\)-open sets. Mat. Vesnik 48, 59–64 (1996)
Arockiarani, I., Lancy, A.A.: Generalized soft \(g\beta \)-closed sets and soft \(gs\beta \)-closed sets in soft topological spaces. Int. J. Math. Arch. 4(2), 1–7 (2013)
Chen, B.: Soft semi-open sets and related properties in soft topological spaces. Appl. Math. Inf. Sci. 7, 287–294 (2013)
Corson, H.H., Michael, E.: Metrizability of certain countable unions. Ill. J. Math. 8, 351–360 (1964)
El-Sheikh, S.A., Abd El-latif, A.M.: Characterization of \(b\)-open soft sets in soft topological spaces. J. New Theory 2, 8–18 (2015)
Han, S.E.: Hereditary properties of semi-separation axioms and their applications. Filomat 32(13), 4689–4700 (2018)
Hussain, S.: On soft regular-open sets (closed) sets in soft topological spaces. J. Appl. Math. Inform. 36(1–2), 59–68 (2018)
Hyland, J.M.E.: Filter spaces and continuous functionals. Ann. Math. Logic 16, 101–143 (1979)
Kandil, A., Tantawy, O.A.E., El-Sheikh, S.A., Abd El-latif, A.M.: \(\gamma \)-operation and decompositions of some forms of soft continuity in soft topological spaces. Ann. Fuzzy Math. Inform. 7(2), 181–196 (2014)
Kuratowski, K.: Topology. Academic Press, New York (1966)
Levine, N.: Semi-open sets and semi-continuity in topological spaces. Am. Math. Mon. 70, 36–41 (1963)
Long, P.: Functions with closed graphs. Am. Math. Mon. 76, 930–932 (1969)
Mashhour, A.S., Abd El-Monsef, M.E., El-Deeb, S.N.: On precontinuous and weak precontinuous mappings. Proc. Math. Phys. Soc. Egypt 53, 47–53 (1982)
Munkres, J.R.: Topology. Prentice-Hall, Upper Saddle River (1975)
Njastad, O.: On some classes of nearly open sets. Pac. J. Math. 15, 961–970 (1965)
Stone, M.: Application of the theory of Boolian rings to general topology. Trans. Am. Math. Soc. 41, 374–481 (1937)
Yumak, Y., Kaymakci, A.K.: Soft \(\beta \)-open sets and their aplications. J. New Theory 4, 80–89 (2015)