# $\mathcal{A}\mathcal{G}_{\I^{*}}$-sets, $ \mathcal{B}G_{\I^{*}}$-sets and $\delta\beta_I$-open sets in ideal topological spaces -by Wadei AL-Omeri and Takashi Noiri

**Abstract:** The aim of this paper is to introduce and study the notions of $ \mathcal{G}_{\I^{*}}$-sets, $\mathcal{A}\mathcal{G}_{\I^{*}}$-sets and $ \mathcal{B}G_{\I^{*}}$-sets sets in ideal topological spaces. Properties of $ \mathcal{G}_{\I^{*}}$-sets, $\delta-C$-sets, $\mathcal{A}\mathcal{G}_{\I^{*}}$-sets, $ \mathcal{B}G_{\I^{*}}$-sets and $\mathcal{E}_{\I^{*}}$-open sets are investigated. Moreover, the relationships among these sets are investigated.

**Keywords: **Ideal topological space, $e$-$\I$-open, $pre^*$-$\mathcal{I}$-open, $semi^*$-$\mathcal{I}$-open, $\mathcal{A}\mathcal{G}_{\I^{*}}$-set, $ \mathcal{B}G_{\I^{*}}$-set, $\delta\beta_I$-open.

**How to cite this article:**

Wadei AL-Omeri and Takashi Noiri, $\mathcal{A}\mathcal{G}_{\I^{*}}$-sets, $ \mathcal{B}G_{\I^{*}}$-sets and $\delta\beta_I$-open sets in ideal topological spaces, International Journal of Advances in Mathematics, Volume 2018, Number 4, Pages 25-33, 2018.