No covering map from $\RP^2$ to the torus

Fundamental-group torsion obstructs a cover from $\RP^2$ to the torus.Suggest a slogan

There is no covering map $p\colon \RP^2 \to \TT^2$.

A covering map induces an injection on fundamental groups [@Hat02], and $\pi_1(\RP^2)\cong\ZZ/2$ does not embed in the torsion-free group $\pi_1(\TT^2)\cong\ZZ^2$.