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 some $\lambda\in F\setminus\{0\}$.

A *line* in $FP^2$ is the image of $L\setminus\{0\}^3$ for some 2-dimensional linear subspace $L$ of $F^3$.

I need a reference to the following results, which (I hope) are true and known:

Theorem 1.Two fields $F_1$ and $F_2$ are isomorphic if and only if there exists a line-preserving bijection between the projective planes $F_1P^2$ and $F_2P^2$.

Theorem 2.Two topological fields $F_1$ and $F_2$ are topologically isomorphic if and only if there exists a line-preserving homeomorphism between the projective planes $F_1P^2$ and $F_2P^2$.

**Remark.** For finite fields, Theorem 1 holds in a stronger form: *two finite fields $F_1$, $F_2$ are isomorphic if and only if there exists a bijection between the projective planes $F_1P^2$ and $F_2P^2$.*