SOME CLASSES IN IDEAL TOPOLOGICAL SPACES

This study presents new classes of open sets defined in ideal topological space. These classes, namely: i - I -open, weakly i- I-open, ii - I -open, and weakly ii -I -open. Also, we gave new concepts of continuity of a mapping between ideal topological spaces using these classes, such as: i –I- continuity weakly i-I-continuity, ii-continuity, and weakly ii-I-continuity. We got their characteristics with comparisons of these classes and concepts. We prove that all open sets, α – I-open, semi - I - open, ii - I-open, weakly semi - I-open, and weakly ii-I-open, sets are weakly i-I-open for any ideal topological space. Additionally, we show that all α –I-continuous, semi-I-continuous, and ii-I-continuous mappings are i-I-continuous. Finally, for ideal topological space (M,L,I) and D ⊂ M satisfying 〖Int(D)〗^#= Int(D), We show that the following statements are equal.:1) D is open 2) D is i-I-open and D∩H = Int(D) for some H ∈ L∖ {M,∅}3) D is semi-I-open. Similarly, We show that the following statements are equal.: 1) D is a closed set, 2) (D∩F) = cl(D) for some F ∈ L^c 3) D is semi-I-closed.