Title: A characterization of sets of <i>n</i> points which determine <i>n</i> hyperplanes
Abstract: Suppose N is a set of points of a d -dimensional incidence space S and { H a }, a ∈ I , a set of hyperplanes of S such that H i ∈ { H a } if and only if H i ∩ N spans H i . N is then said to determine { H a }. We are interested here in the case in which N is a finite set of n points in S and I = {1, 2,…, n }; that is to say when a set of n points determines precisely n hyperplanes. Such a situation occurs in E 3 , for example, when N spans E 3 and is a subset of two (skew) lines, or in E 2 if N spans the space and n − 1 of the points are on a line. On the other hand, the n points of a finite projective space determine precisely n hyperplanes so that the structure of a set of n points determining n hyperplanes is not at once transparent.
Publication Year: 1968
Publication Date: 1968-07-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 31
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