Quotient norm
= Quotient norm
{title2=$\|x+Y\|=\inf_{y\in Y}\|x+y\|$}
The quotient norm measures the smallest norm among representatives of a coset. Its infimum need not be attained. Nevertheless, for every $\varepsilon>0$, an element $z\in X/Y$ has a representative $v\in X$ with $\|v\|<\|z\|+\varepsilon$. The <quotient map> is contractive.