$g^\#$-closed Sets in Ideal Topological Spaces

Abstract

The notion of $g^\#$-closed sets is introduced in ideal topological spaces. Characterizations and properties of $\mathcal{I}_{g^\#}$-closed sets and $\mathcal{I}_{g^\#}$-open sets are given. A characterization of normal spaces is given in terms of $\mathcal{I}_{g^\#}$-open sets. Also, it is established that an $\mathcal{I}_{g^\#}$-closed subset of an $\mathcal{I}$-compact space is $\mathcal{I}$-compact.