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.