Definition:Normed Quotient Vector Space

Definition
Let $\Bbb F \in \set {\R, \C}$.

Let $X$ be a normed vector space over $\Bbb F$.

Let $N$ be a closed linear subspace of $X$.

Let $X/N$ be the quotient vector space of $X$ modulo $N$.

Let $\norm {\, \cdot \,}_{X/N}$ be the quotient norm on $X/N$.

Then we say that $\struct {X/N, \norm {\, \cdot \,} }$ is the normed quotient vector space associated with $X/N$.