About: Luzin space

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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.

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  • 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. (en)
  • 在数学中，以Nikolai Luzin命名的Luzin空间（或Lusin空间）是不可数的拓扑T 1空间，其没有孤立点，每个无处稠密的子集都是可数的。Luzin空间的定义有许多细微的变化：T 1条件可以用T 2或T 3代替，并且一些作者允许空间中存在可数甚至任意数量的孤立点。 (zh)
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  • B. A. (en)
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  • l/l061110 (en)
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  • Efimov (en)
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  • Luzin space (en)
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  • 在数学中，以Nikolai Luzin命名的Luzin空间（或Lusin空间）是不可数的拓扑T 1空间，其没有孤立点，每个无处稠密的子集都是可数的。Luzin空间的定义有许多细微的变化：T 1条件可以用T 2或T 3代替，并且一些作者允许空间中存在可数甚至任意数量的孤立点。 (zh)
  • 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. (en)
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  • Luzin space (en)
  • Luzin space (zh)
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