Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  723.52005
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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