Publications of (and about) Paul Erdös
Autor: Erdös, Paul; Komjáth, P.
Title: Countable decompositions of R2 and R3. (In English)
Source: Discrete Comput. Geom. 5, No.4, 325-331 (1990).
Review: The authors prove that if the continuum hypothesis holds, then R2 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 R3 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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