Duality on locally convex cones

The theory of locally convex cones as a branch of functional analysis was presented by K. Keimel and W. Roth in K. Keimel, W. Roth, Ordered Cones and Approximation, Lecture Notes in Math., vol. 1517, Springer-Verlag, Heidelberg, 1992]. We study some more results about dual cones and adjoint operators on locally convex cones. Moreover we introduce the concept of the uniformly precompact sets and discuss their relations with σ-bounded sets. Some results obtained about inductive limit, projective limit, metrizability and quotients of locally convex cones.