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Axiom of countable choice

Concept in mathematics

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionDec 17, 2025
Entity authoritySource title only
Source-derived summary

The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. That is, given a function with domain such that is a non-empty set for every , there exists a function with domain such that for every .

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The public source identifies “Axiom of countable choice” as concept in mathematics. This brief keeps that definition visible, then builds a research path around Axiom, countable and choice.

Editorial reviewA concise reference frame for defining the subject, testing terminology and identifying the institution closest to the evidence. The current 59-word lead offers orientation but no explicit four-digit date, so chronology should not be assumed. The selected authority fields contribute no independent date. Its value is orientation rather than verdict, with Axiom, countable and choice providing the first useful test.
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This entry incorporates text from “Axiom of countable choice” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.