Urysohn separation property in topological molecular lattices

Abstract

The theory of topological molecular lattices, which is a generalization of the theories of point set topology, fuzzy topology and L-fuzzy topology, is established by Wang. In this paper, the concepts of some kinds of Urysohn separation axioms in topological molecular lattices are introduced and systematically discussed. Several important results, such as the U i (i =−1,0,1,2,3,4) , Urysohn regular and Urysohn normal separation properties are both hereditary and topological invariant, etc., are given.