On generalized topological molecular lattices

• Main Authors: Narges Nazari, Ghasem Mirhosseinkhani
• Format: Article
• Language: English
• Published: University of Maragheh 2018-04-01
• Series: Sahand Communications in Mathematical Analysis
• Subjects: Topological molecular lattice; Generalized Topological molecular lattice; Generalized order homomorphism; Separation axiom
• Online Access: http://scma.maragheh.ac.ir/article_27148_12786ed7e1649bbde8c31adf30c4807c.pdf

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and define a closed element by the pseudocomplement of an open element.  We have two structures on a completely distributive complete lattice, topology and generalized co-topology which are not dual to each other. We study the basic concepts, in particular separation axioms and some relations among them.