Locally convex spaces with all Archimedean cones closed

We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of quasidense set and prove that the above class consists of all finite-dimensional and countable-dimensional spaces $X$ whose topological dual $X'$ is quasidense in the algebraic dual $X^\#$ of $X$.