quotient set

quotient set (plural quotient sets)

1. (mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes

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

• 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”)