For any k deficient matrices there is full column rank matrix to converge

I want to prove the existence of QR decomposition for rank deficient matrices and I am stuck on the step which says that: for any rank-deficient matrix there is a sequence of full-column rank matrices $$A_k$$ such that $$A_k \to A$$ where $$A$$ is a full column rank matrix. I guess that the set of full column rank matrices is compact and therefore there exist a converging subsequence of matrices $$A_k \to A$$ but is it correct?