## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  444.52008
Autor:  Erdös, Paul; Pach, János
Title:  On a problem of L. Fejes Toth. (In English)
Source:  Discrete Math. 30, 103-109 (1980).
Review:  Let 0 \leq x1 \leq x2 \leq x3 \leq ... be a sequence of real numbers, lim xi = +oo. The authors prove that if sumil/xin-k = +oo then there exists a point-system P = {z1,z2,...} in the n-dimensional space En, for which |zi| = xi holds (i = 1,2,...), and any k-dimensional plane comes arbitrarily near to P. this result is best possible in the sense that if P{z1,z2,...} is a point-system satisfying sumil/|zi|n-k <+oo then for every C > 0 there exists a k-dimensional plane in BbbEn, whose distance from all members of P is at least C. A generalization is also proved. This settles a problem of L. Fejes Tóth [Mat. Lapok 25 (1974), 13-20 (1976; Zbl 359.52010)].
Classif.:  * 52A37 Other problems of combinatorial convexity
52A40 Geometric inequalities, etc. (convex geometry)
Keywords:  countable point-system in E2; plane comes arbitrarily near to P
Citations:  Zbl.359.52010

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