In:
Bulletin of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 42, No. 1 ( 1990-08), p. 41-56
Abstract:
Let F be any set of five points in R 3 so situated that no four of the points are coplanar, and that the line xy through any two x and y of the points has a unique intersection point xy * with the plane determined by the other three. Let F^ denote the family of all such xy *. Let S(F) denote the set of all X β F^ which are maximal with respect to the property that X is a subset of a plane in R 3 . For k βͺ 2 an integer, let S ( k ; F ) denote the family of all k -membered elements in S ( F ). A family π of sets is said to be uniformly deep of depth d if and only if for every x β βͺ π there are exactly d distinct π β π for which x β π . We establish the following result, and extend our ideas to general Euclidean spaces.
Type of Medium:
Online Resource
ISSN:
0004-9727
,
1755-1633
DOI:
10.1017/S0004972700028136
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1990
detail.hit.zdb_id:
2268688-5
SSG:
17,1
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