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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