Let $X$ be a metric space and $Y \subseteq X$. For every $a \in X$, $a$ is an interior point of $Y$ if there is $\eps > 0$ such that $\ball_\eps(a) \subseteq Y$. The set of all interior points of $Y$ is called the interior of $Y$:
\[\inter Y = \{a \in X : (\exists \eps > 0 : \ball_\eps(a) \subseteq Y)\}.\]