For any set where denotes the superset with equality holding if and only if the boundary of has no interior points, which will be the case for example if is either closed or open. Since the boundary of a set is closed, for any set The boundary operator thus satisfies a weakened kind of idempotence.
For any set where denotes the superset with equality holding if and only if the boundary of has no interior points, which will be the case for example if is either closed or open. Since the boundary of. a set is closed, for any set The boundary operator thus satisfies a weakened kind of idempotence