Interior point of a set
in a topological space
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 $A$.
Interior point of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior_point_of_a_set&oldid=36945