Question: is rn open or closed?
Answer: A set X ⊂ Rn is closed if its complement Xc = Rn \ X is open. Hence, both Rn and ∅ are at the same time open and closed, these are the only sets of this type. Furthermore, the intersection of any family or union of finitely many closed sets is closed. Note: there are many sets which are neither open, nor closed.