Strongly locally operator

Definition
Suppose $$p$$ is a property of topological spaces. The term strongly locally $$p$$ is used to describe the following property of topological spaces. A topological space $$X$$ is termed strongly locally $$p$$ if for any point $$x \in X$$, and any open subset $$U \ni x$$, there exists an open subset $$V \ni x$$ such that $$\overline{V} \subseteq U$$, and $$V$$ satisfies the property $$p$$.