Some Properties of Alexandrov Topologies
Yong Chan Kim, Young Sun Kim, Young Sun Kim, Young Sun Kim · International Journal of Fuzzy Logic and Intelligent Systems · 2015
Alexandrov topologies are the topologies induced by relations.This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices.With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory.It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.