Theorems on the existence of separating surfaces
Copyright policy )Theorems on the existence of separating surfaces
Let R and G be finite sets in \(E^ d\). Kirchberger's theorem implies that the strict linear separability of R and G is determined by the separability of all subsets of up to \(d+2\) points of \(R\cup G\). This paper shows that under certain conditions, the linear separability of R and G is determined by the separability of significantly fewer than all subfamilies of up to \(d+2\) members of R and G. The same treatment is made of Lay's extension of Kirchberger's theorem to separation by hyperspheres.
- McGill University Canada
- DigiZeitschriften Germany
510.mathematics, Helly's theorem, Kirchberger's theorem, separation of finite sets, Helly-type theorems and geometric transversal theory, Article
510.mathematics, Helly's theorem, Kirchberger's theorem, separation of finite sets, Helly-type theorems and geometric transversal theory, Article
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!