Page 1

Displaying 1 – 10 of 10

Showing per page

Decompositions of the plane and the size of the continuum

Ramiro de la Vega (2009)

Fundamenta Mathematicae

We consider a triple ⟨E₀,E₁,E₂⟩ of equivalence relations on ℝ² and investigate the possibility of decomposing the plane into three sets ℝ² = S₀ ∪ S₁ ∪ S₂ in such a way that each S i intersects each E i -class in finitely many points. Many results in the literature, starting with a famous theorem of Sierpiński, show that for certain triples the existence of such a decomposition is equivalent to the continuum hypothesis. We give a characterization in ZFC of the triples for which the decomposition exists....

Currently displaying 1 – 10 of 10

Page 1