Mohammad Reza Motallebi - University of Mohaghegh Ardabili, Ardabil, Iran.

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.

Products cone topologies, weak cone-completeness, barreledness