On the Krein–Milman–Ky Fan theorem for convex compact metrizable sets

Spline Subdivision Schemes for Convex Compact Sets

The application of spline subdivision schemes to data consisting of convex compact sets with addition replaced by Minkowski sums of sets is investigated These methods generate in the limit set valued functions which can be expressed explicitly in terms of linear com binations of integer shifts of B splines with the initial data as coe cients The subdivision techniques are used to conclude that ...

A convex combinatorial property of compact sets in the plane and its roots in lattice theory

K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...

An embedding theorem for convex fuzzy sets

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

A Representation Theorem for Bounded Convex Sets

A mapping theorem on g-metrizable spaces

In this paper, we give some mapping theorems on g-metrizable spaces in terms of some sequence-covering mappings, σ-mappings and π-mappings.