Document Type : Research Paper
Authors
- Narges Nazari ^{1}
- Ghasem Mirhosseinkhani ^{} ^{2}
^{1} Department of Mathematics, University of Hormozgan, Bandarabbas, Iran.
^{2} Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.
Abstract
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.
Keywords
- Topological molecular lattice
- Generalized Topological molecular lattice
- Generalized order homomorphism
- Separation axiom
Main Subjects
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