Mazurkiewicz's theorem (set theory)

The set of Mazurkiewicz of set theory is a mathematical theorem that the Polish mathematician Stefan Mazurkiewicz back. His proof uses the disintegrated well-order theorem and insofar assumes the validity of the axiom of choice .

The sentence says:

It exists in the Euclidean plane a set of points which with everyone in nearby line has exactly two points in common. ${\displaystyle {\mathbb {E} }^{2}}$ ${\displaystyle {\mathbb {E} }^{2}}$

swell

• Wacław Sierpiński : Cardinal and Ordinal Numbers . Panstwowe Wydawnictwo Naukowe, Warsaw 1958, p. 446-448 . MR0095787