New class of weak open sets via R-interior and a decomposition of continuity

In this paper, some new class of sets R*I-S(X), R*I-P(X) and R*I-α(X) which are the collection of all 'R*I-semi -open', 'R*I -pre-open' and 'R*I-α-open set's are introduced and we analysed how the sets are related with them and examine the relationship the other similar collection of weak open sets in ideal and general topological spaces. Also we obtained an equivalent wayof representing continuous function interms of funcions which are defined using weak open sets in R*-topological spaces.