Soft Closed Sets on Soft Bitopological Space

Yıl 2014, Cilt: 3 Sayı: 5, 57 - 66, 01.05.2014

Guzide Senel Naim Cagman

Öz

Soft set theory was introduced by Molodtsov as ageneral mathematical tool for dealing with problems that containuncertainity. In this paper, on soft bitopological space, we definesoft closed sets; soft α-closed, soft semi-closed, soft pre-closed,regular soft closed, soft g-closed and soft sg-closed. We also giverelated properties of these soft sets and compared their propertieswith each other

Anahtar Kelimeler

-

Kaynakça

• Adnadjevi´c, D.: Ordered spaces and bitopology. Glasnik Mat. Ser. III. 10(30), 337-340 (1975).
• Ayg¨uno˘glu, A., Ayg¨un, H.: Some notes on soft topological spaces. Neu. Comp. and App. 1-7 (2011).
• Ayg¨uno˘glu, A., Ayg¨un, H.: Soft sets and soft topological spaces. preprint. Banaschewski, B., Brummer, G.C.L: Stably continuous frames, Math. Proc. Cam- bridge Philos. Soc. 104, 7-19 (1988).
• Br¨ummer, G.C.L.: Two procedures in bitopology. Categorical Topology (Proc. Internat. Conf., Free Univ. Berlin), 35-43 (1978).
• C¸ a˘gman, N., Engino˘glu, S.: Soft set theory and uni-int decision making, European Journal of Operational Research 10.16/ j.ejor.2010.05.004, 2010.
• C¸ a˘gman, N., Karata¸s, S., Engino˘glu, S.: Soft Topology. Comp. and Math. with App. 62 (1), 351-358 (2011).
• Datta, M.C.: Projective bitopological spaces I. J. Austral. Math. Soc. 13, 327-334 (1972).
• Datta, M.C.: Projective bitopological spaces II. J. Austral. Math. Soc. 14, 119-128 (1972).
• Dvalishvili, B. P.: Bitoplogical Spaces; Theory, Relations with Generalized Alge- braic Structures and Applications. North-Holland Math. Studies 199 (2005).
• Ivanov A. A.: Problems of the Theory of Bitoplogical Spaces (Russian). Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988). Issled.
• Topol. 6, 5-62, 190. English Transl. J. Soviet Math. 52, No:1, 2759-2790 (1990).
• Jafari, S., Thivagar, M.L., Ponmani, S.A: (1, 2)α-open sets based on bitopological seperation axioms. Sooch. J. Math. 33(3), 375-381 (2007).
• Kannan, K.: Soft generalized closed sets in soft topological spaces. J. Theo. and App. Inf. Tech., 37(1), 17-21 (2012).
• Kelly, J. C.: Bitopological Spaces. Proc. London Math. Soc. 13 (3), 71-89 (1963).
• Majumdar, P. ve Samanta, S. K.: On soft mappings. Comp. and Math. with App. 60, 2666-2672 (2010).
• Min, W. K.: A Note on Soft Topological Spaces. Comp. and Math. with App. 62, 3524-3528 (2011).
• Molodtsov, D.A.: Soft set theory-first results. Comp. and Math. with App. 37, 19-31 (1999).
• Patty C. W.: Bitopological Spaces. Duke Math. J. 34, 387-392 (1967).
• Peyghan, E., Samadi, B., Tayebi, A.: On soft connectedness. arXiv: 1202.1668v1 (2012).
• Priestley, H.A.: Ordered topological spaces and the representation of distributive lattices. Proc. London Math. Soc. 24 (3), 507-530 (1972).
• Ravi, O., Thivagar, M.L.,: On stronger forms of (1, 2)∗quotient mappings in bitopological spaces. Internat. J. Math. Game Theory and Algebra. 14(6), 481-492 (2004).
• Ravi, O., Thivagar, M.L.: A bitopological (1, 2)∗Semi-generalized Continuous Maps. Bull. Malays. Math. Sci. Soc(2) 29(1), 79-88 (2006).
• Ravi, O., Thivagar, M.L.: Remarks on extensions (1, 2)∗g-closed mappings in bitopological spaces. preprint. Rong, W.: The countabilities of soft topological spaces. Internat. J. Comp. and Math. Sci. 6, 159-162 (2012).
• Roy, A.R., Maji, P.K.: A fuzzy soft set theoretic approach to decision making problems. J. Comp. Appl. Math. 203, 412-418 (2007).
• Shabir, M., and Naz, M.: On Soft Topological Spaces. Comput. Math. Appl., 61, 1786-1799 (2011).
• Smithson, R.E.: Multifunctions and bitopological spaces. J. Natural Sci. and Math. 11, 191-198 (1971).
• S¸enel, G., C¸ a˘gman, N.: Soft bitopological spaces. submitted. Thivagar, M.L., RajaRajeswari, R.: On bitopological ultra spaces. South. Asian Bull. Math. 31, 993-1008 (2007).
• Zorlutuna, I., and Akda˘g, M., Min, W.K., Atmaca, S.: Remarks on Soft Topolog- ical Spaces. Annals of Fuzzy Math. and Inf. 3 (2), 171-185 (2011).