Lusin space

In mathematics, a Lusin space or Luzin space, named for N. N. Luzin, may mean:

A Lusin space in measure theory and probability, the image of a Polish space under a bijective continuous map. (Some authors add the condition that it should be metrizable.)
A Luzin space in general topology, an uncountable topological T₁-space without isolated points in which every nowhere-dense subset is countable.
A Luzin set in set theory, an uncountable subset of the reals that has at most countable intersection with every nowhere-dense subset of the reals.

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