# Some categorical structures of generalized topologies in terms of monotone operators

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Hormozgan, Bandarabbas, Iran

2 Department of mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran.

10.29252/as.2020.1734

Abstract

In this paper, we give some generalized categories of topological spaces in terms of monotone operators and investigate some categorical properties of them. In particular, we present some equivalent categories of generalized topological spaces in terms of closure and interior operators. Also, we study the properties of some classes of morphisms as  final, initial, closed and open morphisms in these categories.

Keywords

#### References

[1] J. Adamek, H. Herrlich, and G.E. Strecker, Abstract and concrete categories, John Wiely and Sons Inc., New York, 1990.
[2] M.M. Clementino, E. Giuli and W. Tholen, what is a quotient map with respect to a closure operator? Appl. Categ. structures, 9 (2001), 139-151.
[3] A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351-357.
[4] A. Csaszar, Generalized open sets, Acta Math. Hungar., 57 (1-2) (1997), 65-87.
[5] A. Csaszar, Mixed constructions for generalized topologies, Acta Math. Hungar., 122 (2009), 153-159.
[6] A. Csaszar and J.E. Makai, Further remarks on - and -modi catons, Acta Math. Hun-gar., 123 (2009), 223-228.
[7] A. Csaszar, Further remarks on the formula for interior, Acta Math. Hungar., 113 (2006), 325-332.
[8] A. Csaszar, Separation axioms for generalized topologies, Acta Math. Hungar., 104 (2004), 63-69.
[9] J.E. Makai, E. Peyghan and B. Samadi, Weak and strong structures and the T3:5 propertyfor generalized topological spaces, Acta Math. Hungar., 150 (2016), 1-35.
[10] W.K. Min, Generalized continuous functions de ned by generalized open sets on Generalized topological spaces, Acta Math. Hungar., 128 (2010), 299-306.
[11] W.K. Min, Weak continuity on generalized topological spaces, Acta Math. Hungar., 124 (2009), 73-81.
[12] E. Giuli and W. Tholen, Openess with respect to a closure operator, Appl. Categ. structures, 8 (2000), 487-502.
[13] Gh. Mirhosseinkhani, On some classes of quotient maps in closure spaces, Int. Math. Forum, 6 (2011), 1155-1161.
[14] G. Xun and G. Ying, -Separations in generalized topological spaces, Appl. Math. J. Chinese Univ., 25(2) (2010), 243-252.