Quotient Normed Vector Space

Last updated Nov 1, 2022

Let $(X, ||\cdot||)$ be a Normed Vector Space and let $Y \subset X$ be a Closed Vector Subspace. Then we call the Quotient Vector Space $X / Y$ endowed with the Quotient Norm $||[\cdot]||$ Quotient Normed Vector Space.

1. The requirement that $Y$ is Closed is very important. See Quotient Norm