Let Mat(n,k) be the set of nxn matrices with entries in the topological field k. This set can be identified with k^n^2, so it gets a topology.

Let GL(n,k) be the subspace of nxn invertible matrices

My question is, how are open sets defined in this topological space, Mat(n,k)? And is the subspace GL(n,k) defined similarly, the intersection of GL(n,k) with all open sets of Mat(n,k)?