Quotient Normed Space of a Banach Space is Banach

Last updated Nov 1, 2022

Let $(X, ||\cdot||)$ be a Banach Space and let $Y \subset X$ be a Closed Vector Subspace. Then the Quotient Normed Vector Space $(X / Y, ||[\cdot]||)$ is a Banach Space.

TODO use

• A Metric Space is Complete iff all Absolutely Convergent Series Converge
• Use Quotient Norm definition to get close and then use Quotient Map is a Contraction Operator