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About: Sierpiński set     Goto   Sponge   NotDistinct   Permalink

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Type: Thingprogramming language New Facet based on Instances of this Class

In mathematics, a Sierpiński set is an uncountable subset of a real vector space whose intersection with every measure-zero set is countable. The existence of Sierpiński sets is independent of the axioms of ZFC. Sierpiński showed that they exist if the continuum hypothesis is true. On the other hand, they do not exist if Martin's axiom for ℵ1 is true. Sierpiński sets are weakly Luzin sets but are not Luzin sets .