Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes (Q1311015)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes |
scientific article; zbMATH DE number 484130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes |
scientific article; zbMATH DE number 484130 |
Statements
Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes (English)
0 references
13 January 1994
0 references
Let \(k\) be any natural number. The author shows that each subset \(V\) of Euclidean 3-space \(E^ 3\) (which spans \(E^ 3\) affinely) with at least \(4k+1\) points possesses some subset spanning a plane \(J\) such that each open half-space determined by \(J\) contains at least \(k\) points of \(V\).
0 references
Helly-type
0 references
separation of points
0 references
