Separating hyperplanes for convex sets over ordered fields (Q1059111)
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: Separating hyperplanes for convex sets over ordered fields |
scientific article; zbMATH DE number 3902782
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Separating hyperplanes for convex sets over ordered fields |
scientific article; zbMATH DE number 3902782 |
Statements
Separating hyperplanes for convex sets over ordered fields (English)
0 references
1984
0 references
Let \((F,<)\) be an ordered field. Theorem. If A,B are disjoint convex sets in \(F^ n\), then the ordering of F can be extended to an ordering of the rational function field \(K=F(t_ 1,...,t_ n)\) in such a way that A,B are strongly separated by a hyperplane in \(K^ n\).
0 references
separating hyperplanes
0 references
ordered field
0 references
convex sets
0 references
ordering of the rational function field
0 references
