The category of soft topological spaces and the \(T_0\)-reflection

Volume 22, Issue 1, pp 1--8 http://dx.doi.org/10.22436/jmcs.022.01.01

Publication Date: June 05, 2020 Submission Date: March 05, 2020 Revision Date: April 09, 2020 Accteptance Date: April 23, 2020

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Authors

Abdelwaheb Mhemdi - Department of Mathematics, Faculty of Sciences and Humanities in Aflaj, Prince Sattam Bin Abdul-Aziz University, Kingdom of Saudi Arabia.

Abstract

Soft topological spaces represent the objects of a category named SOFTOP. In this paper, we will study some properties of arrows in SOFTOP. We give also the construction of the \(T_0\)-reflection of a soft topological space illustrated by other results related to separation axioms.

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Keywords

• Soft set
• soft topological spaces
• reflective subcategory
• separation axioms

MSC

•  06D72
•  54A40
•  54D10

References

• [1] K. Belaid, O. Echi, S. Lazaar, $T_{(\alpha, \beta)}$-spaces and the Wallman compactification, Int. J. Math. Math. Sci., 2004 (2004), 3717--3735
  • View Article
  • MathSciNet
  • MATH


• [2] N. Cagman, S. Karatas, S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011), 351--358
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] D. G. Chen, E. C. C. Tsang, D. S. Yeung, X. Z. Wang, The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49 (2005), 757--763
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] D. N. Georgiou, A. C. Megaritis, Soft set theory and topology, Appl. Gen. Topol., 15 (2014), 93--109
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] D. N. Georgiou, A. C. Megaritis, V. I. Petropoulos, On soft topological spaces, Appl. Math. Inf. Sci., 7 (2013), 1889--1901
  • View Article
  • MathSciNet
  • Google Scholar


• [6] A. Grothendieck, Éléments de géométrie algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math., 4 (1960), 228 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] A. Grothendieck, J. A. Dieudonné, Eléments de géométrie algébrique, Springer-Verlag, Berlin (1971)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] H. Herrlich, G. Strecker, Categorical topology--Its origins as exemplified by the unfolding of the theory of topological reflections and coreflections before 1971, in: Handbook of the history of general topology, 1997 (1997), 255--341
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] S. Hussain, B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., 62 (2011), 4058--4067
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] H.-P. A. Künzi, T. A. Richmond, $T_i$-ordered reflections, Appl. Gen. Topol., 6 (2005), 207--216
  • View Article
  • MathSciNet
  • MATH


• [11] S. Lazaar, A. Mhemdi, On some properties of $T_{0}-$ordered reflection, Appl. Gen. Topol., 15 (2014), 43--54
  • View Article
  • MATH


• [12] S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, New York (1971)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555--562
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077--1083
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] W. K. Min, A note on soft topological spaces, Comput. Math. Appl., 62 (2011), 3524--3528
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19--31
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] D. A. Molodtsov, V. Y. Leonov, D. V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1 (2006), 8--39
  • View Article
  • Google Scholar


• [18] D. Pei, D. Miao, From soft sets to information systems, IEEE Int. Conf. Granular Comput., 2005 (2005), 617--621
  • View Article
  • Google Scholar


• [19] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786--1799
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] I. Zorlutuna, M. Akdag, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171--185
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH