Is the region $x^2+y^2 \geq 1$ open or closed

Question

Is the region $x^2+y^2 \geq 1$ open or closed , both open and closed or neither open nor closed?

Closed region is a set of points which contains it's boundary points while open region only contains its interior points excluding boundary points. So what should we take here in the case of infinite set? Is there any definition set for empty and infinite sets?

Answer 1

This is a definitely closed set, since $x^2 + y^2 < 1$ is an open set, and your set is the complement set.