# A note on product topologies in locally convex cones

Document Type : Research Paper

Author

University of Mohaghegh Ardabili, Ardabil, Iran.

10.22103/jmmrc.2021.18239.1170

Abstract

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.

Keywords

#### References

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### History

• Receive Date: 16 September 2021
• Revise Date: 07 December 2021
• Accept Date: 07 December 2021