Interior of a Set
If
is a subset of a set
then the interior of the setis written
and is equal to
where
is the closure of
We write
We can also think of the interior of a set in terms of open sets. The interior of a setis the largest open set containing A. We can write
Example: Suppose
with the usual metric
on 
A has no interior since there are no open sets inwith the usual metric, so
Proof
Suppose
and
are equivalent statements. If D subset A then X-A subset X-D=C. Since is open, C is closed.
We obtain
