Rotation through any nonzero angle defines a continuous self-map of a circular annulus with no fixed point. Hence an annulus does not have the fixed-point property.
Articles by others on the same topic
In mathematics, an annulus (plural: annuli) is a ring-shaped object that is formed by the region between two concentric circles. It can be described in the following way: 1. **Definition**: An annulus is the set of points in a plane that are situated between two circles, typically denoted by an inner circle with radius \( r_1 \) and an outer circle with radius \( r_2 \), where \( r_2 > r_1 \).