a) A point is a boundary point of iff every neighborhood around contains points in and . A point is a boundary point of iff every neighborhood around contains points in and . What can you conclude from this?

b) A point is an interior point of iff there exists a neighborhood around that is a proper subset of . Compare this definition with the above definition and deduce that .

c) If is open, then every point in is an interior point, so . is trivially true.

If , then , meaning that every point in is an interior point, so is open.