# Closed set, open set or neither?

Just a quick question - is a straight line that goes on indefinitely viewed as a closed set, open set or neither? Seeing as it includes all the boundary points as it travels, but it doesn't have any end points.

(E.g. $y = 2x$)

• Note that "open" and "closed" are not mutually exclusive. However, since the plane is connected, the only sets that are both open and closed are the entire plane $\Bbb R^2$ and the empty set $\emptyset$. – Akiva Weinberger Jan 25 '16 at 17:14