Some notes on bornological and nonbornological locally convex cones

Abstract

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.

Keywords

• Locally convex cones
• Nonbornological Cones