Every finite-dimensional real vector space has a unique Hausdorff topology making it a topological vector space. Choosing a basis identifies it with ordinary Euclidean space; every linear map between such spaces is continuous.
On a finite-dimensional vector space over a complete valued field, any two norms induce the same topology. Choosing a basis reduces the claim to comparison with the maximum of the absolute values of the coordinates.
Articles by others on the same topic
There are currently no matching articles.