Convexity conditions for non-locally convex lattices

Convexity Conditions for Non - Locally Convex Lattices

for any x 1 ( . . . , x,, GX. A theorem of Aolci and Rolewicz (see [18]) asserts that if in (1.3) C = 2~\ then X is p-normable. We can then equivalently re-norm X so that in (1.4) JB = 1. If in addition X is a vector lattice and ||x||<||y|| whenever |x|<|y| we say that X is a quasi-Banach lattice. As in the case of Banach lattices [13] we may make the following definitions. We shall say that X ...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

approximate convexity and submonotonicity in locally convex spaces

On locally convex PL-manifolds and fast verification of convexity

We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. O...

Beyond convexity: scanning 'non-convex polyhedra'

The enumeration of points contained in an algebraically specified domain is one of the key algorithmic problems in the transformation of scientific programs. However, basic scanning algorithms accept only single convex polyhedra, requiring specialized techniques and causing run-time overhead if the set of points to enumerate is not convex. In this paper, we review the existing approaches to the...