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

Abstract

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