  We present a general way to define a topology on orthomodular lattices. We
show that in the case of a Hilbert lattice, this topology is equivalent to that
induced by the metrics of the corresponding Hilbert space. Moreover, we show
that in the case of a boolean algebra, the obtained topology is the discrete
one. Thus, our construction provides a general tool for studying orthomodular
lattices but also a way to distinguish classical and quantum logics.
