On -continuous and -irresolute Maps in Topological Spaces

On pre­ Open Regular Spaces

“…P.C(Z)) and say that a set H in a space Z is preclosed neighborhood [11][12][13] of a point c if H is preclosed and contains a pre-open set to which c belongs. For each pair of topological spaces Z and Y a function f: Z→Y is called pre-irresolute 14,15…”

Theory of g-T_g-Maps

“…The concepts 1 of (T Ω , T Σ )-map π : T Ω → T Σ [1,2], g-(T Ω , T Σ )-map π g : T Ω → T Σ [9,18], (T g,Ω , T g,Σ )-map π : T g,Ω → T g,Σ [3], and g-(T g,Ω , T g,Σ )-map π g : T g,Ω → T g,Σ [21], called, respectively, ordinary and generalized maps (briefly, T-map and g-T-map, respectively) between T -spaces T Ω and T Σ , and ordinary and generalized maps (briefly, T g -map and g-T g -map, respectively) between T g -spaces T g,Ω and T g,Σ are all fundamental concepts that have been introduced and investigated by several mathematicians [12,16,17,20,21,23,29,31,33].…”