Search

Bornological and b-bornological locally convex cones have studied in [D. Ayaseh and A. Ranjbari, Bornological Locally Convex Cones, Le Matematiche, Vol. LXIX (2014) Fasc. II, pp. 267-284]. In this paper, we obtain new results on bornological locally convex cones and present an example of nonbornological locally convex cone. We show that the projectivelimit of bornological cones is not bornological in general. Also, we present a bornological locally convex cone which is not b-bornological.

In this paper we define bornological and b-bornological cones and investigate their properties. We give some characterization for these cones. In the special case of locally convex topological vector space both these concepts reduce to the known concept of bornological spaces. We introduce and investigate the convex quasiuniform structures U_{tau}, U_{sigma}(P,P*) and \U_{beta}(P,P*) on locally convex cone (P,U).