English Dictionary

axiom of choice

名詞

可算名詞 不可算名詞

(set theory) One of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.

日本語の意味

集合論における公理の一種であり、任意の非空集合の族から各集合の要素を選ぶことで形成される直積集合が非空であることを保証する原理。

Many proofs in topology implicitly rely on the axiom of choice.

位相空間論の多くの証明は、暗黙のうちに選択公理に依存している。

意味（1）

(set theory) One of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.

The axiom of choice is logically equivalent to the assertion that every vector space has a basis.

axioms of choice （ plural ）