generic point

Let $X$ be a topological space and suppose that $x\in X$. If for all $y\in X\backslash \backslash \{x\}$ we have $x\notin \overline{\{y\}}$ then we say that $x$ is a generic point. Equivalently, $x$ is generic iff it is not a specialization point of any point in $X$, other than $x$ itself.