This paper is devoted to the study of H_1 topological molecularlattices, a generalization of the Hausdorff fuzzy topological spaces.Some primary properties of such topological molecular lattices arediscussed For any complete and completely distributive lattice L, theexistence and uniqueness of minimal H_1 co-topologies on L areinvestigated, and the characteristic theorem of minimal H_1co-topologies on L is established.
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