# Interior point of a set

A point $x$ of a given set $A$ in a topological space for which there is an open set $U$ such that $x \in U$ and $U$ is a subset of $A$. If $x$ is an interior point of a set $A$, then $A$ is said to be a neighbourhood of the point $x$ in the broad sense. The interior of a set $A$ consists of the interior points of $A$.