The notion of operations on a topological space was introduced 

by S.Kasahara [8].  The notions of generalized continuous functions [1] 

and T$_{1/2}$-spaces [12] are further investigated using operation 

approaches [14].  

As applications, it is shown that the Khalimsky line (=the digital 

line)[9] and  two kinds of "digital picture" with a topology are 

typical examples of "Int$\circ$Cl"-T$_{1/2}$ spaces.