quotient set

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English

Noun

quotient set (plural quotient sets)

(mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes
Given the set of integers $\mathbb {Z}$ , and the equivalence relation $a\sim b\iff a\equiv b(\mod 2)\iff (a-b)\%2=0$ , the quotient set is written $\mathbb {Z} /\sim =\{{\bar {0}},{\bar {1}}\}$ , consisting of the even and the odd integers.

Translations

set of all equivalence classes

See also

quotient topology (“a topology on a quotient set derived from a topology on the generating set”)
quotient space (“a topological space constructed by endowing the quotient set with its quotient topology”)

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