Quotient Banach space
= Quotient Banach space
{title2=$X/Y$}
For a closed <vector subspace> $Y$ of a <Banach space> $X$, the <quotient vector space> $X/Y$ is complete with its <quotient norm>. Closedness makes the quotient seminorm a norm. Completeness follows by choosing representatives of a rapidly Cauchy subsequence whose successive differences have summable norms in $X$.