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It is a compact, smooth manifold of dimension 3, and is a special case Gr(1, R 4) of a Grassmannian space. RP 3 is (diffeomorphic to) SO(3), hence admits a group structure; the covering map S 3 → RP 3 is a map of groups Spin(3) → SO(3), where Spin(3) is a Lie group that is the universal cover of SO(3).
Ado (Japanese: アド, [α] born October 24, 2002) is a Japanese singer and songwriter. In 2020, at the age of 17, she made her debut with the digital single titled "Usseewa", which peaked at number 1 on Billboard Japan Hot 100, [4] Oricon Digital Singles Chart, and the Oricon Streaming Chart. [5]