Generalized Mappings And Generalized Open Sets In Topology

In topology, the class of subsets is studied extensively, including the class of open sets, semi-open sets, feebly open set.α-open sets,β-open sets, semi-prcopen sets. Owing to the fact that the corresponding definitions have many features in common, so A.Csaszar defines generalized open sets to study these sets for integration. In addition, A.Csaszar defines locally closed sets, locally regular sets, and studies the properties of the generalized mapping r from subset to subset, r∈ΓΔ, Δ∈(0,1,2,-2,3,+,-)(ΓΔ is the class of mapping from subset to subset).In this paper, combining with the concepts of generalized open sets, gener-alized mapping, closed sets, regular sets, we define a new class Γ4of mappings, locally closed sets and locally regular sets. We also study the properties of Γ4, the combination of Γ4and ΓΔ(Δ∈0,1,2,-2,3+,-), and the properties of generalized locally closed sets and generalized regular sets.