# Cantor-Bendixson theorem

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## English

### Proper noun

Cantor-Bendixson theorem

1. (set theory) A theorem which states that a closed set in a Polish space is the disjoint union of a countable set and a perfect set.
From the Cantor-Bendixson theorem it can be deduced that an uncountable set in ${\displaystyle \mathbb {R} }$ must have an uncountable number of limit points.