Let $H$ be Hilbert space and denote set of all orthogonal projections in $H$ by $\Pi$. Then $\Pi$ can be given structure of a lattice. We partially order it by declaring $P \leq Q$ if $Q-P$ is nonnegative operator. Then it becomes complete, orthomodular lattice. Some further properties can be found in http://planetmath.org/latticeofprojections
Question is: are the join and meet operations continuous? The answer might depend on choice of one of standard operator topologies (obviously). If that is the case I am interested in all three: norm, strong and weak.