Abstract
In this paper, first we give some characterizations and properties of strong beta-I-open sets. Then, we obtain a decomposition of semi-I-closed sets by using strong beta-I-open sets and t-I-sets. In addition, we give decompositions of open sets in any extremally disconnected space and in any ideal topological space. Moreover, we define AK(I)-set and AK(I)*-set and give decompositions of continuity.