A circle is bounded becauseSolutionThe maximum distance betw

A circle is bounded because...

Solution

The maximum distance between two points on a circle or a sphere is the diameter. So it is bounded.

The function X^2 + y^2 is continuous and the circle is the inverse image of a point, other than zero. For example the circle of radius 1 is the inverse image of 1. But a point on the real line is closed and the inverse image of a closed set under a continuous map is also closed.