Yong Ming LI(1),De Xue ZHANG(2
It is proved in this paper that for a TO topological molecular lattice (L,η), the following conditions are equivalent: (1) (L, η) is a regular injective TO topological molecular lattice; (2) L is a complete set ring and of which the set of complete coprimes forms a continuous lattice, and η is the Scott co-topology on the continuous lattice of complete coprimes; (3) There exists an injective TO space such that (L, η) is homeomorphic to the Soberification (in the sense of topological molecular lattice) of (P(X),TC). Besides, the structures of (not necessarily TO) regular injective topological molecular lattices, the structures of general injective topological molecular lattices and that of regular injective molecular lattices are also given. As applications, a new (and simple) proof of the structures of exponentiable topological molecular lattices is given.