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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 11th 2017

    added a quick note on the CW-structure on real projective space: here.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 11th 2017

    Another very common (and slightly different) realization is inductive, via pushouts of type

    S n1 D n quot ℝℙ n1 ℝℙ n\array{ S^{n-1} & \to & D^n \\ \mathllap{quot} \downarrow & & \downarrow \\ \mathbb{R P}^{n-1} & \hookrightarrow & \mathbb{R P}^n }

    where quotquot divides by the /2\mathbb{Z}/2-action.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 11th 2017

    The complex analogue of that happens to be discussed at complex projective space, here.