Edit: According to the comment of L. Spice I changed the inclusion sign to the subset sign.

Is there a continuous map $f:\mathbb{C}P^3 \to Gr_{\mathbb{C}}(2,4)$ with $x\subset f(x)$? What about a map $g$ in the opposite direction with $g(x)\subset x$? What about a holomorphic version ($f$ or $g$ holomorphic)? What about a generalization about such maps between arbitrary grassmanian spaces?