We have been presented a new definition of dense and found relationships between them. Also, we put a new definition of the submaximal depending on of the weakly-I-dense. It is through the definitions above we have also introduce a new types of resolvable spaces and we discuss the hereditarily irresolvable and open hereditarily irresolvable and we got the relationships between them. We study a new types of the first category, Baire space, new closure operator depending on of the local function of M*, and we introduce a new definition of resolvable space under the idea of the e-dense and the relationships between them. Finally we provide a new definition of the first category and Baire space and investigating relationships between them.