Search: MSC category 46A30 ( Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) )
 Products and Direct Sums in Locally Convex Cones In this paper we define lower, upper, and symmetric completeness and discuss closure of the sets in product and direct sums. In particular, we introduce suitable bases for these topologies, which leads us to investigate completeness of the direct sum and its components. Some results obtained about $X$-topologies and polars of the neighborhoods. Keywords:product and direct sum, duality, locally convex coneCategories:20K25, 46A30, 46A20