RELATIONS AND GENERALIZED TOPOLOGIES

In this paper, we study generalized topological spaces derived from binary relations.
Pretopological spaces and neighborhood spaces are two forms of generalized topological spaces. It is shown that neighborhood spaces and pretopological spaces can be generated from families of binary relations. We try to find out the necessary and sufficient conditions that must be stated on families of binary relations under which the spaces generated by such families be (R0), (T0) and (T1) spaces. Many other properties of these spaces are discussed.