Originally Posted by

**Sheld** Proposition 1.

Let $\displaystyle (X,d) $ be a metric space, then

a) The sets $\displaystyle X$ and $\displaystyle \emptyset$ are open

Similarly,

Proposition 2.

Let $\displaystyle (X,d)$ be a metric space, then

a) The sets $\displaystyle X$ and $\displaystyle \emptyset$ are closed.

However, I have no clue why a) is listed for both and why a) is important. What is a) telling us? If someone could please explain to me the meaning of a) in both cases it would be much appreciate.