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Are there two infinite dimensional (Banach or Hilbert) manifolds $(P,L)$ which satisfy the axioms of a smooth projective geometry desribed in this page: Smooth Projectove Geometry

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    $\begingroup$ If X and Y are two non-isomorphic Banach spaces would their projectivizations P(X) and P(Y) be examples of what you ask for? I'm not sure, just a thought. $\endgroup$
    – alvarezpaiva
    Commented Apr 12, 2020 at 17:35

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