Categories of lattice-valued closure (interior) operators and Alexandroff L-fuzzy topologies

Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

2 Department of Mathematics, Liaocheng University, Liaocheng, 252059 P.R. China and College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P.R.China.

Abstract

Galois connection in category theory play an important role in
establish the relationships between different spatial structures. In
this paper, we prove that there exist many interesting Galois
connections between the category of Alexandroff $L$-fuzzy
topological spaces, the category of reflexive $L$-fuzzy
approximation spaces and the category of Alexandroff $L$-fuzzy
interior (closure) spaces. This indicates that there is a close
connection between the three structures.

Keywords


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