University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401On generalized topological molecular lattices1152714810.22130/scma.2017.27148ENNargesNazariDepartment of Mathematics, University of Hormozgan, Bandarabbas, Iran.GhasemMirhosseinkhaniDepartment of Mathematics, Sirjan University of Technology, Sirjan, Iran.Journal Article20161220In 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.http://scma.maragheh.ac.ir/article_27148_12786ed7e1649bbde8c31adf30c4807c.pdf