Generalized topological representation for complete join-semilattices (Q397032)

The well-known adjunction between topological spaces and frames is extended to that between generalized topological spaces and complete join-semilattices. Here, generalized topological spaces are taken in the sense of Császár, i.e., given by a set of subsets closed under unions. There are also discussed lattice theoretic counterparts of separation axioms of generalized topological spaces extending those known for frames.