We prove that any compact topological orthomodular lattice
is zero dimensional. This leads one to show that
is profinite iff it is the product of finite orthomodular lattices with their discrete topologies. We construct a completion
of a residually finite orthomodular lattice
having the property that every element of
is the join of meets of elements of
. Necessary and sufficient conditions for
is the MacNeille completion are obtained.