- Proceedings of International Mathematical Sciences
- Vol: 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 Motallebi
Pages : 11-15
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Publication Date : 2019-06-15
Article Type : Research
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