Normed vector space/Translation/Continuous/Exercise

Let ${}V$ be a normed ${}{\mathbb {K} }$-vector space, and let

$\varphi _{w}\colon V\longrightarrow V,v\longmapsto v+w,$

denote the translation with the vector ${}w\in V$. Show that ${}\varphi _{w}$ is continuous.

Create a solution