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Oct 9, 2014 at 18:34 comment added Bjørn Kjos-Hanssen @GejzaJenča That's not what I was claiming. The question is a bit hard to read but I took it to mean that $L$ is a lattice of projections but not necessarily the lattice of all projections. So $L$ corresponds to a set of subspaces closed under intersection and join.
Oct 9, 2014 at 18:05 comment added Gejza Jenča It is not true that the coordinate planes in $R^3$ are orthogonal or comparable to all other subspaces. Proof: take any plane that is not among the coordinate planes.
Oct 7, 2014 at 8:38 vote accept King Kong
Oct 6, 2014 at 13:22 history answered Bjørn Kjos-Hanssen CC BY-SA 3.0