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