Prove that A^0 U B^0 is a subset of the interior of A U B
Let and be subsets of with , denoting the sets of interior points for and respectively. Prove that is a subset of the interior of . Give an example where the inclusion is strict.
Let and be subsets of with , denoting the sets of interior points for and respectively. Prove that is a subset of the interior of . Give an example where the inclusion is strict.
Recall that the interior of a set is the largest open subset of a set.
The union of two open sets is open. So what about
Is that union a open subset of