Last edit
Changed:
< We will discuss the following property of compact convex sets: nonempty intersection of an arbitrary class of translations of a set is a summand (in the Minkowski sense) of the set. We will show that some sets different to polyhedron and ellipsoid, such as wedges, blunt wedges and some parts of the Euclidean ball also own the property in question. Moreover, we will prove that the family of all three-dimensional strongly monotypical polyhedrons coincide with the family of all three-dimensional polyhedral sets having the above property.
to
> We will discuss the following property of compact convex sets: nonempty intersection of an arbitrary class of translations of a set is a summand (in the Minkowski sense) of the set. We will show that some sets different to polyhedron and ellipsoid, such as wedges, dull wedges and some parts of the Euclidean ball also own the property in question. Moreover, we will prove that the family of all three-dimensional strongly monotypical polyhedrons coincide with the family of all three-dimensional polyhedral sets having the above property.
Danuta Borowska and Jerzy GrzybowskiIntersection property in the class of all closed bounded and convex sets.
We will discuss the following property of compact convex sets: nonempty intersection of an arbitrary class of translations of a set is a summand (in the Minkowski sense) of the set. We will show that some sets different to polyhedron and ellipsoid, such as wedges, dull wedges and some parts of the Euclidean ball also own the property in question. Moreover, we will prove that the family of all three-dimensional strongly monotypical polyhedrons coincide with the family of all three-dimensional polyhedral sets having the above property.