A topological approach to soft groupoids

Gulay Oguz

doi:10.5269/bspm.51392

Gulay Oguz Harran University

Abstract

In this manuscript, the notion of soft topological groupoid is proposed by examining in a dierent perspective the notion of soft groupoid, which is defined as a parameterized family of the subgroupoids of a soft groupoid. In this context, topological groupoid structures are equipped with soft set theory and the category of soft topological groupoids is formed. Subsequently, the definition of soft topological subgroupoid is presented and all new notions given are strengthened by illustrative examples.

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References

D. A. Molodtsov, Soft set theory-First results, Comput. Math. Appl., 37(4-5), 19-31, (1999). https://doi.org/10.1016/S0898-1221(99)00056-5

P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45(4-5), 555-562, (2003). https://doi.org/10.1016/S0898-1221(03)00016-6

A. Aygunoglu, A. Aygun, Some notes on soft topological spaces, Neural Comput. Appl., 22(1), 113-119, (2012). https://doi.org/10.1007/s00521-011-0722-3

H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci., 77(13), 2726-2735, (2007). https://doi.org/10.1016/j.ins.2006.12.008

A. O. Atagun, A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61(3), 592--601, (2011). https://doi.org/10.1016/j.camwa.2010.12.005

U. Acar, F. Koyuncu , B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, 3458- 3463, (2010). https://doi.org/10.1016/j.camwa.2010.03.034

G. Oguz, I. Icen, M.H. Gursoy, Actions of Soft Groups, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68, 1163-1174, (2019). https://doi.org/10.31801/cfsuasmas.509926

M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61(7), 1786-1799, (2011). https://doi.org/10.1016/j.camwa.2011.02.006

N. Cagman, S. Karatas, S. Enginoglu, Soft topology, Comput. Math. Appl., 62(1), 351-358, (2011). https://doi.org/10.1016/j.camwa.2011.05.016

T. Shah, S. Shaheen, Soft topological groups and rings, Ann. Fuzzy Math. Inform., 7(5), 725-743, (2014).

W. K. Min, A Note on Soft Topological Spaces, Comput. Math. Appl., 62, 3524-3528, (2011). https://doi.org/10.1016/j.camwa.2011.08.068

R. Brown, 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).

R. Brown, Topology and Groupoids, BookSurge LLC, North Carolina, (2006).

H. Nurusev, Topological grupoids, M.Sc.Thesis, Gazi University, Ankara, Turkey, (1995).

G. Oguz I. Icen, M. H. Gursoy, A New Concept in the Soft Theory : Soft Groupoids, SEA bull. math., 44, 555-565, (2020).

O. Zahiri, Category of soft sets, Ann. Uni. Craiova Math. Comp. Sci. Ser., 40(2), 154-166, (2013).

S. K. Sardar, S. Gupta, Soft category theory-an introduction, Journal of Hyperstructures, 2, 118-135, (2013).

O. Zahiri, Category of soft sets, Ann. Uni. Craiova Math. Comp. Sci. Ser., 40 , 154-166, (2013).

L. A. Zadeh, Fuzzy sets, Inf.Control, 8, 338-353, (1965). https://doi.org/10.1016/S0019-9958(65)90241-X

Z. Pawlak, Rough Sets, Int. J. Comput. Inf. Sci., 11, 341-356, (1982). https://doi.org/10.1007/BF01001956

G. Oguz, Soft Topological Transformation Groups, Mathematics, 8, 1545, (2020). https://doi.org/10.3390/math8091545