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On soft topological categories

Year 2019, Volume: 48 Issue: 6, 1675 - 1681, 08.12.2019

Abstract

In this paper, we introduce the notion of a soft topological category as a natural consequence of the existence of topological category and soft category. Some examples of the soft topological categories are given. The properties of soft topological category are investigated and some important results are obtained. Also, the notion of topological functor is extended to the notion of soft topological functor. Finally, we present some examples about it.

References

  • [1] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59, 3458–3463, 2010.
  • [2] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci. 77 (13), 2726-2735, 2007.
  • [3] A. Aygunoglu and A. Aygun, Some notes on soft topological spaces, Neural Comput. Appl. 22 (1), 113-119, 2012.
  • [4] R. Brown and T. Porter, Category Theory: an abstract setting for analogy and comparison, in: What is Category Theory? Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy, 257–274, 2006.
  • [5] N. Cagman, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl. 62 (1), 351–358, 2011.
  • [6] P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (4-5), 555–562, 2003.
  • [7] W.K. Min, A Note on Soft Topological Spaces, Comput. Math. Appl. 62, 3524–3528, 2011.
  • [8] D.A. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37 (4-5), 19–31, 1999.
  • [9] H. Nurusev, Topological grupoids, M.Sc. Thesis, Gazi University, Ankara, Turkey, 1995.
  • [10] S. Oztunc, Some properties of soft categories, Int. J. Model. Optim. 6 (2),2016.
  • [11] S.K. Sardar and S. Gupta, Soft category theory-an introduction, J. Hyperstruct. 2, 118–135, 2013.
  • [12] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (7), 1786–1799, 2011.
  • [13] T. Shah and S. Shaheen, Soft topological groups and rings, Ann. Fuzzy Math. Inform. 7 (5), 725–743, 2014.
  • [14] O. Zahiri, Category of soft sets, An. Univ. Craiova Ser. Mat. Comput. Sci. 40 (2), 154-166, 2013.
Year 2019, Volume: 48 Issue: 6, 1675 - 1681, 08.12.2019

Abstract

References

  • [1] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59, 3458–3463, 2010.
  • [2] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci. 77 (13), 2726-2735, 2007.
  • [3] A. Aygunoglu and A. Aygun, Some notes on soft topological spaces, Neural Comput. Appl. 22 (1), 113-119, 2012.
  • [4] R. Brown and T. Porter, Category Theory: an abstract setting for analogy and comparison, in: What is Category Theory? Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy, 257–274, 2006.
  • [5] N. Cagman, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl. 62 (1), 351–358, 2011.
  • [6] P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (4-5), 555–562, 2003.
  • [7] W.K. Min, A Note on Soft Topological Spaces, Comput. Math. Appl. 62, 3524–3528, 2011.
  • [8] D.A. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37 (4-5), 19–31, 1999.
  • [9] H. Nurusev, Topological grupoids, M.Sc. Thesis, Gazi University, Ankara, Turkey, 1995.
  • [10] S. Oztunc, Some properties of soft categories, Int. J. Model. Optim. 6 (2),2016.
  • [11] S.K. Sardar and S. Gupta, Soft category theory-an introduction, J. Hyperstruct. 2, 118–135, 2013.
  • [12] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (7), 1786–1799, 2011.
  • [13] T. Shah and S. Shaheen, Soft topological groups and rings, Ann. Fuzzy Math. Inform. 7 (5), 725–743, 2014.
  • [14] O. Zahiri, Category of soft sets, An. Univ. Craiova Ser. Mat. Comput. Sci. 40 (2), 154-166, 2013.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Gülay Oğuz This is me 0000-0003-4302-8401

M. Habil Gürsoy 0000-0003-3576-0731

İlhan İçen

Publication Date December 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 6

Cite

APA Oğuz, G., Gürsoy, M. H., & İçen, İ. (2019). On soft topological categories. Hacettepe Journal of Mathematics and Statistics, 48(6), 1675-1681.
AMA Oğuz G, Gürsoy MH, İçen İ. On soft topological categories. Hacettepe Journal of Mathematics and Statistics. December 2019;48(6):1675-1681.
Chicago Oğuz, Gülay, M. Habil Gürsoy, and İlhan İçen. “On Soft Topological Categories”. Hacettepe Journal of Mathematics and Statistics 48, no. 6 (December 2019): 1675-81.
EndNote Oğuz G, Gürsoy MH, İçen İ (December 1, 2019) On soft topological categories. Hacettepe Journal of Mathematics and Statistics 48 6 1675–1681.
IEEE G. Oğuz, M. H. Gürsoy, and İ. İçen, “On soft topological categories”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1675–1681, 2019.
ISNAD Oğuz, Gülay et al. “On Soft Topological Categories”. Hacettepe Journal of Mathematics and Statistics 48/6 (December 2019), 1675-1681.
JAMA Oğuz G, Gürsoy MH, İçen İ. On soft topological categories. Hacettepe Journal of Mathematics and Statistics. 2019;48:1675–1681.
MLA Oğuz, Gülay et al. “On Soft Topological Categories”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, 2019, pp. 1675-81.
Vancouver Oğuz G, Gürsoy MH, İçen İ. On soft topological categories. Hacettepe Journal of Mathematics and Statistics. 2019;48(6):1675-81.