O-C topology and Sierpinski space

Abstract EN

In this paper we choose a different approach and propose a generalization of Sierpinski space by defining a topology analogous to Sierpinski topology with the general collection  which is form a topology on a non empty set  , and the definition of K.

Khan [5] will be only special case , so the ( O-C topology) is introduced .

We investigate some of the general topological characterization of it , and this has a very interesting applications especially the Sierpinski space which is result from the finite set  which containing only two points .