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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 723.52005

**Autor: ** Erdös, Paul; Komjáth, P.

**Title: ** Countable decompositions of **R**^{2} and **R**^{3}. (In English)

**Source: ** Discrete Comput. Geom. 5, No.4, 325-331 (1990).

**Review: ** The authors prove that if the continuum hypothesis holds, then **R**^{2} can be decomposed into countably many pieces, none spanning a right-angled triangle. They also obtain some partial results concerning the conjecture that the given result is also true when `right- angled' is replaced by `isosceles'. Finally, they show that **R**^{3} can be coloured with countably many colours with no monochromatic rational distance.

**Reviewer: ** E.J.F.Primrose (Leicester)

**Classif.: ** * 52C10 Erdoes problems and related topics of discrete geometry

51M15 Geometric constructions

**Keywords: ** decomposition; right-angled triangle; isosceles

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