$b^{\ast}_{I}$ Sets and $b^{\ast}_{I}$-Compact Ideal Spaces

We came up with the concept b∗-open set which has stricter condition with respect to the notion b-open sets, introduced by Andrijevic [2] as a generalization of Levine’s [7] generalized closed sets. The condition imposes equality instead of inclusion. In this study, we gave some important properties of b∗-open sets with respect to an ideal, and b∗-compact spaces.