Canad. Math. Bull. 55(2012), 783-798
Printed: Dec 2012
M. R. Motallebi,
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.
product and direct sum, duality, locally convex cone
20K25 - Direct sums, direct products, etc.
46A30 - Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
46A20 - Duality theory