Solution
= Solution
The <Brouwer fixed-point theorem> says that every continuous self-map of the closed unit disc has a fixed point.
A union of two disjoint closed discs does not have the <fixed-point property>. Define a map that is constant from the first component to a point in the second and constant from the second component to a point in the first. It is continuous because the components are disjoint and has no fixed point.