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 $f:(X,\mathrm{\Gamma })\to (Y,\tau )$, where $(X,\mathrm{\Gamma })$ is a resolvable generalized topological space and $(Y,\tau )$ is a nondiscrete Moore space. We also present some properties of set of points of path continuity with respect to $(\mathrm{\Gamma },\mathcal{T})$ for functions $f:(X,\mathrm{\Gamma })\to (Y,\varrho )$, where $(X,\mathrm{\Gamma })$ is a generalized topological space, $\mathcal{T}$ is a topology associated with Γ and $(Y,\varrho )$ is a nondiscrete metric space. Some relevant properties of continuity and path continuity are discussed.

2002年Á。Császár介绍了广义拓扑的概念，该概念与拓扑的概念有所不同，因为缺少交集属性。在广义拓扑中，许多类型的广义连续性都可以视为连续性，例如拟连续性，预连续性，多孔连续性，定性连续性，Denjoy性质。在本文中，我们全面描述了函数的广义连续性的点集$F：（X，\mathrm{\Gamma }）\to （ÿ，\tau ）$， 在哪里 $（X，\mathrm{\Gamma }）$ 是一个可解析的广义拓扑空间， $（ÿ，\tau ）$是一个非离散的摩尔空间。我们还介绍了相对于$（\mathrm{\Gamma }，\mathcal{Ť}）$ 用于功能 $F：（X，\mathrm{\Gamma }）\to （ÿ，\varrho ）$， 在哪里 $（X，\mathrm{\Gamma }）$ 是广义的拓扑空间， $\mathcal{Ť}$ 是与Γ关联的拓扑 $（ÿ，\varrho ）$是一个非离散的度量空间。讨论了连续性和路径连续性的一些相关属性。