Any Orthocomplemented Complete Modular Lattice is a Continuous Geometry

Summary:Let $alpha$ be an infinite cardinal. Let $Cal T_alpha$ be the class of all lattices which are conditionally $alpha$-complete and infinitely distributive. We denote by $Cal{T}_sigma'$ the class of all lattices $X$ such that $X$ is infinitely distributive, $sigma$-complete and has the least element. In this paper we deal with direct factors of lattices belonging to $Cal T_alpha$. As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class $Cal T_sigma'$