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For a (topological) field $F$ by $FP^2$ we denote the projective plane, i.e., the quotient space of $F^3\setminus\{0\}^3$ by the equivalence relation $\vec x\sim\vec y$ iff $\vec x=\lambda\vec y$ for for $\lambda\in F\setminus\{0\}$.
A line in $FP^2$ is the quotient image of $L\setminus\{0\}^3$ ...
