Abstract
In this paper, we introduce the notions of $\alpha_{\gamma}$-interior, $\alpha_{\gamma}$-neighbourhood, $\alpha_{\gamma}$-derived, $\alpha_{\gamma}$-boundary, $\alpha_{\gamma}$-kernel and $\alpha$-$\gamma$-g.closed set defined by $\gamma$-operation on $\alpha O(X)$ and investigate some of their properties.
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