Definition · applies to sets · also called $\operatorname{int} A$, $A^{\circ}$

Elementary

The interior of a shape is the part on its inside, not including its edge.

Undergraduate (subsets of $\reals^n$)

A point $x$ is in the interior of $A$ if there exists an open ball around $x$ that is contained in $A$.

Graduate (topological spaces)

The interior of $A$ is the union of all open sets contained in $A$: the largest open subset of $A$.

Properties

  • A set is open if and only if it equals its interior.
  • The interior, boundary, and exterior of a set are disjoint, and together they make up the whole space.

All definitions · All distinctions · All examples