In this paper, $(X, \tau, \mathcal{I})$ denotes an ideal topological space. Analogously to the local function \cite{JH}, we define an operator $\Gamma(A)(\mathcal{I},\tau)$ called the local closure function of $A$ with respect to $\mathcal{I}$ and $\tau$ as follows: $\Gamma(A)(\mathcal{I},\tau)=\{x\in X:A\cap Cl(U)\notin \mathcal{I}\text{ for every }U \in \tau(x)\}$. We investigate properties of $\Gamma(A)(\mathcal{I},\tau)$. Moreover, by using $\Gamma(A)(\mathcal{I},\tau)$, we introduce an operator $\Psi_\Gamma:\mathcal{P}(X)\rightarrow\tau$ satisfying $\Psi_\Gamma(A)=X-\Gamma(X-A)$ for each $A\in\mathcal{P}(X)$. We set $\sigma=\{A\subseteq X:A\subseteq\Psi_{\Gamma}(A)\}$ and $\sigma_0=\{A\subseteq X:A\subseteq Int(Cl(\Psi_\Gamma(A)))\}$ and show that $\tau_\theta\subseteq\sigma\subseteq\sigma_0$.