Density of Infimum-Stable Convex Cones

Bornological Completion of Locally Convex Cones

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.

Rough convex cones and rough convex fuzzy cones

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

The Infimum of the Volumes of Convex Polytopes

We prove the theorem mentioned in the title, for Rn, where n ≥ 3. The case of the simplex was known previously. Also, the case n = 2 was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolic n-spaces. There we give some necessary conditions for the existence of a convex polytope with given facet areas, and some ...

Geometric Tomography of Convex Cones

The parallel X-ray of a convex set K ⊂ R in a direction u is the function which associates to each line l parallel to u the length of K ∩ l. The problem of nding a set of directions such that the corresponding X-rays distinguish any two convex bodies has been widely studied in geometric tomography. In this paper we are interested in the restriction of this problem to convex cones, and we are mo...

Some Results on Boundedness in Locally Convex Cones