Linear mapping/Normed spaces/Finite-dimensional/Continuity/Fact

Let ${}V$ and ${}W$ be normed ${}{\mathbb {K} }$-vector spaces, and let

$\varphi \colon V\longrightarrow W$

denote a linear mapping. Let ${}V$ be finite-dimensional.

Then ${}\varphi$ is continuous.

Proof, Write another proof