Application of ic—open Sets in Topologies Via Ideals

Abstract

In this paper, new kinds of open sets inside ideal topological spaces are introduced; they are called ic - I - open,icc - I -open,weakly ic - I - open and weakly icc - I - open. Some properties and relations between these new classes are studied with examples. The concept of continuity in ideal topological spaces is also presented for these new classes. Theorems that provide an equivalence relation between these new classes are proved. Also, for ideal topological spaces (Ɲ, Ʈ, I) we show that all open sets are ic -I- open, icc - I - open, weakly ic - I - open, weakly icc - I - open . Finally, Assume Z ⊂ Ɲ of ideal Topological spaces (Ɲ,Ʈ,l ). Then 1) if Z is semi - I - open, then Zc is ic – I - open.2) if Z is open and ic - I - closed, then Z is semi - I - open.

Keywords

• ideal topological space
• ic-i-open
• icc-i-open