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Theory of topological molecular lattices. (English) Zbl 0783.54032
The theories of point set topology, fuzzy topology and \(L\)-fuzzy topology, are brought into a unified theory – the theory of topological molecular lattices (TML). The minimal family theory and the maximal family theory in a complete lattice are studied. If \(L\) is a completely distributive lattice and \(M\) is the set of all \(\vee\)-irreducible elements except 0 then the elements of \(M\) are called molecules and \(L\) is a molecular lattice. For such lattices the concepts of closed elements, closed topology (co-topology), remote-neighbourhoods, molecular nets are introduced. The theory of pointwise topology on molecular lattices is developed. Convergence, continuity, countability, separability, separation axioms, connectivity and quasi-uniformity are investigated.

MSC:
54H12 Topological lattices, etc. (topological aspects)
54A40 Fuzzy topology
06B30 Topological lattices
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