Bornological Convergence in Locally Convex Cones

In this paper we define bornological and b-bornological convergence in locally convex cones. We give some characterizations for these convergences. In special case of locally convex topological vector spaces, both these concepts reduce to the known concept of Mackey-convergence. We investigate the relationship between bornological cones and bornological convergence. Finally, we investigate bornological completeness.