Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  182.33101
Autor:  Erdös, Pál
Title:  Geometrical and set-theoretical properties of subsets of Hilbert-space (In Hungarian)
Source:  Mat. Lapok 19, 255-257 (1968).
Review:  The author proved in a previous paper without assuming the continuum-hypothesis that if S is a subset of an n-dimensional space then S contains a subset S1 of power m so that all the distances between points of S1 are distinct. C × t o-by, Kakatuani and the author showed that if P is any denumerable dense set of positive numbers then there is a set H in a Hilbert space of power \aleph1 so that all the distances between points in H are in P, further there is a set H1 of power C in Hilbert space so that all the distances between points in H1 are the square root of a rational number. We do not know if all the distances can be rational.
Is it true that if H is a set of power m in a Hilbert space then H has a subset of power m which does not contain an equilateral triangle?
Classif.:  * 46C05 Geometry and topology of inner product spaces
Index Words:  set theory

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