# Are any two isomorphic normed linear spaces homeomorphic?

We know that any two finite-dimensional linear spaces (over a same field) of same dimension is isomorphic.

Qn.1 Are any two finite-dimensional normed linear spaces (over a same field) with same dimension isometrically isomorphic?

Qn.2 Are any two isomorphic normed linear spaces are homeomorphic?

• Answer to Qn 1. $\mathbb R^{2}$ with Euclidean norm is not isometrically isomorphic to $\mathbb R^{2}$ with the max norm. – Kavi Rama Murthy Apr 11 at 10:25
2. Any two finite dimensional normed linear spaces (of the same dimension) are homeomorphic, because any two convex,compact sets in $$\mathbb{R}^n$$ with non-empty interior are homeomorphic one to another.