Document Type: Research Paper


Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.


In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.


[1] D. Ayaseh and A. Ranjbari, Bornological convergence in locally convex cones, Mediterr. J. Math., 13 (2016), pp. 1921-1931.

[2] D. Ayaseh and A. Ranjbari, Bornological locally convex cones, Le Matematiche, 69 (2014), pp. 267-284.

[3] D. Ayaseh and A. Ranjbari, Completion of a locally convex convex cones, Filomat, 31 (2017), pp. 5073--5079.

[4] D. Ayaseh and A. Ranjbari, Locally convex quotient lattice cones, Math. Nachr., 287 (2014), pp. 1083-1092.

[5] S. Jafarizad and A. Ranjbari, Openness and continuity in locally convex cones, Filomat 31 (2017), pp. 5093-5103.

[6] K. Keimel and W. Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer Verlag, Heidelberg-Berlin-New York, 1992.

[7] A. Ranjbari and H. Saiflu, Projective and inductive limits in locally convex cones, J. Math. Anal. Appl., 332 (2007), pp. 1097-1108.

[8] W. Roth, Operator-valued measures and integrals for cone-valued functions, Lecture Notes in Mathematics, vol. 1964, Springer Verlag, Heidelberg-Berlin-New York, 2009.