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Quotient Set

The quotient set of a set X by an equivalence relation ∼ is the set of its equivalence classes,

X/∼={[x]:x in X},

where [x]={y in X:y∼x}. The canonical projection q:X->X/∼ sends each element to its equivalence class. A function on X that is constant on equivalence classes factors uniquely through q.

See also

Equivalence Class, Equivalence Relation, Partition, Quotient Space

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References

Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974.

Cite this as:

Weisstein, Eric W. "Quotient Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/QuotientSet.html

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