Put $P=[0,1]$.Is there a compact subset $L$ of the hyper space of $P$ such that the pair $(P, L)$ satisfy the following axioms of projective geometry and the obvious maps from the canfiguration space of $P$ to $L$ and configuration space of $L$ to $P$ would be continuous?

http://mathoverflow.net/questions/261436/non-isomorphic-projective-planes-on-omega