Öz
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.
Anahtar Kelimeler
soft set soft topological group category functor soft category soft topological category
Kaynakça
- [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.
Öz
Kaynakça
- [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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 8 Aralık 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 48 Sayı: 6 |