$\ast -$open sets and $\ast -$ continuity in topological spaces

In this paper, we study some properties of $\ast -$open and $\ast -$closed subsets of a space. The collection of all $\ast -$open subsets of a space $X$ form a topology on $X$ which is denoted by ${}^{\ast }O(X)$. We investigate the relations between topological properties of $X$ with the topology ${}^{\ast }O(X)$ and $X$. Also, we introduce the concept of a $\ast -$continuous map.