Properties of Theta-Continuous Functions in Topological Spaces

Velicko [1968] introduced the concepts of θ - closure and θ - interior operations. The collection of all θ - open sets in a topological space X forms a topology on X. In this paper we introduce θ - irresolute, θ - closed, pre-θ -open, and pre-θ -closed mappings and investigate properties and characterizations of these new types of mappings. We also explore further properties of the well-known notions of θ - continuous and θ - open mappings.