I have shown any norms on a finite dimensional real vector space are equivalent then the question asks why would this imply every finite-dimensional subspace of normed vector space is closed. (Closed in the sense that it is toplogically closed, its complement is an open subset.)
I understand that equivalent norms yield the same notion of convergence however I have very few ideas on where to start. I have seen a few posts showing the subspace is complete instead, but I do not think it is in the spirit of this problem.
How should I proceed? Many thanks in advance!