Countable decompositions ofR2 andR3
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If the continuum hypothesis holds,R2 is the union of countably many sets, none spanning a right triangle. Some partial results are obtained concerning the following conjecture of the first author:R2 is the union of countably many sets, none spanning an isosceles triangle. Finally, it is shown thatR3 can be colored with countably many colors with no monochromatic rational distance.
KeywordsDiscrete Comput Geom Isosceles Triangle Continuum Hypothesis Density Zero Countable Collection
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