On continuity in generalized topology

Abstract

In 2002 Á. Császár introduced the notion of generalized topology, which differs from the notion of topology by the lack of the intersection property. Many kinds of generalized continuity may be considered as a continuity in a generalized topology, for example quasicontinuity, precontinuity, porouscontinuity, qualitative continuity, Denjoy property. In the paper we give full characterization of set of points of generalized continuity for functions f:(X,Γ)→(Y,τ), where (X,Γ) is a resolvable generalized topological space and (Y,τ) is a nondiscrete Moore space. We also present some properties of set of points of path continuity with respect to (Γ,T) for functions f:(X,Γ)→(Y,ϱ), where (X,Γ) is a generalized topological space, T is a topology associated with Γ and (Y,ϱ) is a nondiscrete metric space. Some relevant properties of continuity and path continuity are discussed.