Soft topology in ideal topological spaces

Abstract

In this paper, $(X, \tau, E)$ denotes a soft topological space and $\overline{\mathcal{I}}$ a soft ideal over $X$ with the same set of parameters $E$. We define an operator $(F, E)^{\theta}(\overline{\mathcal{I}}, \tau)$ called the $\theta$-local function of $(F, E)$ with respect to $\overline{\mathcal{I}}$ and $\tau$. Also, we investigate some properties of this operator. Moreover, by using the operator $(F, E)^{\theta}(\overline{\mathcal{I}}, \tau)$, we introduce another soft operator to obtain soft topology and show that $\tau_{\theta}\subseteq\sigma\subseteq\sigma_{0}$.