Soft I-sets and Soft I-Continuity of Functions

The topic of ideals in general topological spaces is treated in the classic text by Kuratowski [6]. This topic has an excellent potantial for applications in other branches of mathematics. The Cantor-Bendixson Theorem examplies this potantial. This subject was continued to study by general topologists in recent years [6; 11; 15; 17] : Kale and Guler [8] gave the denition of soft ideal in the soft topological spaces and studied some properties. In this paper, the soft I-continuous and soft I-open functions, has been defined and studied. Some characterizations and several properties concerning these functions are obtained.

___

  • D. Moldtsov, Soft set theory-First results, Computers and Mathematics with Applications, 37 (1999) 19-31.
  • M. Shabir and M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61 (2011) 1786-1799.
  • A. Kharal and B. Ahmad, Mappings on soft classes, Computation, Vol.7 No.3 (2011) 471-481. and Natural
  • A. Aygunoglu and H. A. Aygun, Some notes on spaces, soft topological Natural Computer
  • H. Hashimoto, On the ∗topology and its
  • applications, Fund. Math., (1976) 91, 5-10.
  • T.R. Hamlett and D. Jankovic, Ideals in topological spaces and the set operator Ψ, Bollettino U.M.I., (1990) vol. 7, 863-874.
  • M.E. Abd El-Monsef, E.F. Lashien and A.A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math. J., (1992) vol. 32 (1), 21-30
  • E. Hatır and T. Noiri, On semi-I-continuous sets and semi-I-continuous functions, Acta. Math. Hungar., (2005), 107 (4), 345-353.
  • D. Jankovic, T.R. Hamlett, Compatible extensions of ideals, Boll. Un. Mat. Ital. (7), 6-B (1992) 453- 465.
  • E. Hatır and T. Noiri, On decompositions o fcontinuity via idealization, Acta. Math. Hungar., 96 (2002), 341-349.
  • J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2 (1996).
  • G. Kale and A.Caksu Guler, On Soft Ideal Topological Spaces, Neural Computing and Applications, 1-14.
  • F. Feng, Y.B. Zhao, Soft semirings, Computer and Mathematics with Applications, 56 (2008), 2621- 2628.
  • P.K. Maji, B. Biswas and A.R. Roy, Soft set theory, Applications, 45 (2003), 555-562. Mathematics with
  • M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Computer and Mathematics with Applications, 57 (2009), 1547-1553.
  • I. Zorlutuna, M. Akdag, W.K. Min and S. Atmaca, Remarks on soft topological spaces, to appear in Annals of Fuzzy Mathematics and Informatics.
  • W. Rong, The countabilities of soft topological spaces, International Journal of Computational and Mathematical Sciences, 6 (2012).
  • J. Mahanta, P.K. Das, On soft topological space via semiopen and semiclosed soft sets.
  • A. Kandil, O.A.E. Tantawy, S.A. El-Sheikh, A.M. Abd El-Latif, γoperation and decomposition of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 2013.