Descriptive set theory | Properties of topological spaces

Luzin space

In mathematics, a Luzin space (or Lusin space), named for N. N. Luzin, is an uncountable topological T1 space without isolated points in which every nowhere-dense subset is countable. There are many minor variations of this definition in use: the T1 condition can be replaced by T2 or T3, and some authors allow a countable or even arbitrary number of isolated points. The existence of a Luzin space is independent of the axioms of ZFC. showed that the continuum hypothesis implies that a Luzin space exists. showed that assuming Martin's axiom and the negation of the continuum hypothesis, there are no Hausdorff Luzin spaces. (Wikipedia).

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Related pages

Real closed field | Outer measure | Vector space | Isolated point | Sierpiński set | T1 space | Hausdorff space | Field extension | Descriptive set theory | Real analysis | Mathematics | Continuum hypothesis | Meagre set | Wacław Sierpiński | Subset | Subgroup | Measure (mathematics) | Separation axiom | Martin's axiom