On topology expansions by ideals and applications

The topology τ of a space is enlarged to a topology τ* using an ideal P whose members are disjoint with the members of τ. Many relations between topological concepts with respect to τ and τ* are obtained. For example τ and τ* have identical classes of dense (pre-open) subsets, semi-Ti, i {0,1,2}, semi-Ri, i {0,1}, and semi-T′2 are preserved from τ and τ* and vice versa. Preservation of some sorts of compactness and closeness is discussed.