Antipodal map

Definition
Let $$X$$ and $$Y$$ be two spaces, each equipped with antipode maps, both denoted by $$-$$. Then, a antipodal map between $$X$$ and $$Y$$ is a continuous map that commutes with the antipode. In other words, $$f:X \to Y$$ is antipodal if $$f(-x) = -f(x)$$.