In this paper, we present concepts of pre ��p-open sets and pre ��p-
closures of a subset in a topological space, where ��p is an operation on the family
of all preopen sets of the topological space, and study some topological properties
on them. As its application, we introduce the concept of pre ��p-Ti spaces (i =
0; 1=2; 1; 2) and study some properties of these spaces.