A note on product topologies in locally convex cones

Abstract

We consider the locally convex product cone topologies and prove that the product topologyof weakly cone-complete locally convex cones is weakly cone-complete. In particular, we deduce that a product cone topology is barreled whenever its components are weaklycone-complete and carry the countable neighborhood bases.

Keywords

• products cone topologies
• weak cone-completeness
• barreledness