FΣ Set

(Descriptive Set Theory)

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sciences
Descriptive Set Theory
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What is Fσ set?

In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in France with F for fermé (French: closed) and σ for somme (French: sum, union). In metrizable spaces, every open set is an Fσ set. The complement of an Fσ set is a Gδ set. In a metrizable space, any closed set is a Gδ set. The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set. Fσ is the same as in the Borel hierarchy.

Technology Types

descriptive set theorytopology

Synonyms

F sigmaF sigma setF-sigmaF-sigma set

Translations

Ensemble F-sigma (fr)F-сигма-множество (ru)F-сігма-множина (uk)Fσ集 (zh)Fσ集合 (ja)Zbiór typu F-sigma (pl)

Tech Info


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