When an operator gives a unique generalized topology

الموضوعات :

N. Sarkar ¹ (Department of Mathematics, Raiganj University, 733134, Raiganj, India)
A. Das ² (Department of Mathematics, Raiganj University, 733134, Raiganj, India)
T. E. Aman ³ (Department of Mathematics, Gangarampur College, 733124, Gangarampur, India)

تاريخ الإرسال : 22 الخميس , رمضان, 1444 تاريخ التأكيد : 07 السبت , ذو القعدة, 1444 تاريخ الإصدار : 12 الخميس , ذو القعدة, 1444

الکلمات المفتاحية: Generalized topology, $\mu$-interior, $\mu$-derived set, $\mu$-exterior, $\mu$-boundary,

ملخص المقالة :

In topology, we found enough literature on topological operators but in generalized topology, there is only $\mu$-interior, $\mu$-closure, and $\mu$-boundary operator. In this article, we explore different types of operators like $\mu$-derived set operator, $\mu$-exterior operator, $\mu$-preboundary operator in generalized topology. We have shown that any operator can be developed as the above operators impose certain conditions, giving a unique generalized topology in each case.

المصادر:

[1] A. Császár, Generalized open sets, Acta. Math. Hungar. 75 (1997), 65-87.

[2] A. Császár, Generalized open sets in generalized topologies, Acta. Math. Hungar. 106 (2005), 53-66.

[3] A. Császár, Generalized topology generalized continuity, Acta. Math. Hungar. 96 (2002), 351-357.

[4] N. Elez, O. Papaz, The new operators in topological space, Mathematica Moravica. 17 (2) (2013), 63-68.

[5] R. Khayyeri, R. Mohamadian, On base for generalized topological spaces, Int. J. Contemp. Math. Sciences. 48 (2011), 2377-2383.

[6] R. D. Sarma, On convergence in generalized topology, Int. J. Pure. Appl. Math. 60 (2) (2010), 51-60.