A note on product topologies in locally convex cones

Document Type : Research Paper


University of Mohaghegh Ardabili, Ardabil, Iran.


We consider the locally convex product cone topologies and prove that the product topology
of 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 weakly
cone-complete and carry the countable neighborhood bases.


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  • Receive Date: 16 September 2021
  • Revise Date: 07 December 2021
  • Accept Date: 07 December 2021
  • First Publish Date: 08 December 2021