Sierpiński set

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 (1924) 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 (Kunen 2011, p. 376).

单词	Sierpinski set
释义	Sierpinski set 英语百科 Sierpiński set 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 (1924) 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 (Kunen 2011, p. 376).
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Sierpinski set

Sierpiński set