----- > [!proposition] Proposition. ([[degree of the antipodal map]]) > The [[antipodal map]] $a:\mathbb{S}^{n} \to \mathbb{S}^{n}$ given by $a(x_{1},\dots,x_{n+1}) = -x_{1},\dots,-x_{n+1}$ > has [[degree of a continuous map on the sphere|degree]] $(-1)^{n+1}$ because it is a composition of $(n+1)$ [[reflection|reflections]], and [[the degree of a reflection is -1]]. ^proposition ----- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```