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 $p$.