A subspace of $\mathbb R^n$ is compact if and only if it is closed and bounded in the Eulidean Metric or Square Metric or $l_1$ metric.
Is my statement correct?
Actually the statement - "A subspace of $\mathbb R^n$ is compact iff it is closed and bounded in the Euclidean Metric or Square Metric" was given in Mukresh. I think closed and bounded set in the $l_1$ metric would also be compact. As the topologies of three are same.
Am I correct? Please correct me if I am wrong.