> I am not sure whether I understand you correctly. Does the proof uses the > assumption that the map sends parallel lines to parallel lines?
Yes. When you say that a map T sends straight lines into straight lines, I take it this means that all the points of l are mapped into all the points of T(l). In that case, if T(l) and T(m) meet in P then P must be on l and m, which therefore are not parallel.
-- Timothy Murphy e-mail: gayleard /at/ eircom.net School of Mathematics, Trinity College, Dublin 2, Ireland