= Quotient topological space
{title2=$X/{\sim}$}
A quotient topological space identifies points of a <topological space> according to an <equivalence relation> and equips the set of equivalence classes with the <quotient topology>. A subset is open exactly when its inverse image under the canonical <quotient map> is open. Even a <Hausdorff space> can have a non-Hausdorff quotient; identifying real numbers differing by a rational number gives a multi-point quotient with the <indiscrete topology>.
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