Weak Cone-Completeness of Direct Sums in Locally Convex Cones

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Proceedings of International Mathematical Sciences
Volume:1 Issue:1
Weak Cone-Completeness of Direct Sums in Locally Convex Cones

Weak Cone-Completeness of Direct Sums in Locally Convex Cones

Authors : Mohammad Reza MOTALLEBİ

Pages : 11-15

View : 29 | Download : 12

Publication Date : 2019-06-15

Article Type : Research Paper

Abstract :We consider the weak cone-completeness in locally convex cones and prove that the direct sum of a family of weakly cone-complete separated locally convex cones is weakly cone-complete. We conclude that a direct sum cone topology is barreled whenever its components are weakly cone-complete and separated with the countable bases.
Keywords : Locally convex cones, direct sums, weak cone completeness

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