Sadi BAYRAMOV, Çiğdem GÜNDÜZ ARAS, Nesrin DEMIRCI

SOFT TOPOLOJİK UZAYLARIN TERS SİSTEMLERİ

Many practical problems in economics, engineering, environment, social science, medical science etc. cannot be dealt with by classical methods, because classical method have inherent difficulties. The reason for these difficulties may be due to the inadequacy of the theories of parameterization tools. Molodtsov initiated the concept of soft set theory as a new mathematical tool for dealing with uncertainties. Research works in soft set theory and its applications in various fields have been progressing rapidly since Maji et al. The idea of soft topological spaces was first given by M. Shabir, M. Naz and mappings between soft sets were described by P. Majumdar, S.K. Samanta. Later, many researches about soft topological spaces were studied in . In these studies, the concept of soft point is expressed by different approaches. In the study we use the concept of soft point which was given in [14]. Soft topological spaces and soft continuous mapping form category and this category is extension of category of topological spaces. Also category of fuzzy topological spaces is extension of category of topological spaces. In this article the closure problem is investigated according to algebraic operation in the category of soft topological spaces. For this, the existence of limits of inverse systems of soft topological spaces is proven.

Keywords:

Soft topological spaces, topological spaces,

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[1] U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, (2010) 3458-3463.
[2] H. Aktaş, N. Çağman, Soft sets and soft group, Information Science, 177, (2007) 2726-2735.
[3] A. Aygunoglu, H. Aygun, Some notes on soft topological spaces, Neural Comput & Applic, DOI: 10.1007/s00521-011-0722-3, 2011.
[4] S. Bayramov, C. Gunduz (Aras), Inverse and direct systems in the category of intuitionistic fuzzy M-groups, İntern. Math. Forum, 19(4), (2009) 897-918.
[5] S. Bayramov, C. Gunduz (Aras), On isomorphism theorems of fuzzy soft groups, ICMS, Bolu, Turkey, (2010) 23-27.
[6] S. Bayramov, C. Gunduz (Aras) and M. İ. Yazar, Inverse systems of fuzzy soft modules, Annals of Fuzzy Mathematics and Informatics, 4(2), (2012) 349-363.
[7] S. Bayramov, C. Gunduz (Aras) and T. Y. Ozturk, Homology theory in the category of fuzzy topological spaces, Lambert Academic Publishing, 143 p, (2012) Deutscland, Germany.
[8] S. Bayramov, Fuzzy and fuzzy soft structure in algebra, Lambert Academic Publishing, 175 p, (2012) Deutscland, Germany.
[9] N. Çağman, S. Karataş, S. Enginoğlu, Soft topology, Comput. Math. Appl., 62, (2011) 351-358.
[10] F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl.,56(10), (2008) 2621-2628.
[11] C. Gunduz (Aras) , B. Davvaz, The universal coefficient theorem in the category of intuitionistic fuzzy modules, Utilitas Math., 81, (2010) 131-156.
[12] C. Gunduz (Aras), S. Bayramov, Fuzzy soft modules, International Mathematical Forum, 6(11), (2011) 517-527.
[13] C. Gunduz (Aras), S. Bayramov, Intuitionistic fuzzy soft modules, Computers and Mathematics with Applications, 62, (2011) 2480-2486.
[14] C. Gunduz (Aras), S. Bayramov, Soft locally compact and soft paracompact spaces, Journal of Mathematics and System Science, 2, (2013).
[15] C. Gunduz (Aras), S. Bayramov, Intuitionistic fuzzy soft topological spaces, TWMS Pure Appl. Math. V5, 1, (2014) 66-79.
[16] S. Hussain, B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., 62, (2011) 4058-4067.
[17] A. Kharal, B. Ahmad, Mappings of soft classes, to appear in New Math. Nat. Comput.
[18] P. K. Maji, R. Bismas, A. R. Roy, Fuzzy soft sets, The Journal of Fuzzy Mathematics, 9(3), (2001) 589-602.
[19] P. K. Maji, A. R. Roy, R. Bismas, An Aplication of soft sets in a decision making problem, Comput. Math. Appl., 44, (2002) 1077-1083.
[20] P. K. Maji, R. Bismas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45, (2003) 555-562.
[21] W. K. Min, A note on Soft topological spaces, Comput. Math. Appl., 62, (2011) 3524-3528.
[22] D. Molodtsov, Soft set theory- first results, Comput. Math. Appl., 37, (1999) 19-31.
[23] A. R. Roy, P. K. Maji, A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, 203, (2007) 412-418.
[24] H. Sabir, A. Bashir, Some properties of soft topological spaces, Comput. Math. Appl., 62, (2011) 4058-4067.
[25] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61, (2011) 1786-1799.
[26] Qiu-Mei Sun, Zi-Liong Zhang, Jing Liu, Soft sets and soft modules, Lecture Notes in Comput. Sci., 5009, (2008) 403-409.
[27] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965) 338-353.
[28] I. Zorlutuna, M. Akdağ, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2), (2012) 171-185.