Given a topological space (X,\tau) an ideal \mathcal{I} on X and A \subseteq X. The concept of a-local function defined as follows A^{a^\ast}(\mathcal{I},\tau)=\{x \in X: U \cap A \notin \mathcal{I}, \,\text{for every}\,\, U \in \tau^{a}(x)\}. In this paper a new type of space has been introduced with the help of a-open sets and the ideal topological space called \textbf{a}-ideal space. Also we introduce an operator \Re_a : \wp(X)\rightarrow \tau have been discussed, for every A \in \wp(X). We utilize the \Re_a- operator to define interesting generalized a-open sets and study their properties.

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Al-Omari, Wadei Faris, Noorani, Mohd Salmi Md., Noiri, T., Al-Omeri, A.