Definition:Normed Quotient Vector Space
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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 $X/N$.
Also see
- Results about normed quotient vector spaces can be found here.