Antipode map

Definition
An antipodal map on a topological space is an involutive homeomorphism from the topological space satisfying the following conditions:


 * It has no fixed points
 * The quotient map of the topological space by the equivalence relation of being equal or antipodal to each other, is a covering map of degree two

For instance, the map that sends a point in the sphere to its usual antipode (that is, the opposite with respect to the center) is an antipodal map.