[:compact in R^n iff closed + bounded:] • JRM:Top.2 §27.3 • Take some subspace topology $A \subseteq \mathbb R^n$. Then TFAE: • $A$ is compact$A$ is closed and $A$ is bounded using the euclidean metric $d$$A$ is closed and $A$ is bounded using the square metric $\rho$ • Equivalence of the final two essentially come from that $\rho \leq d \leq \rho \sqrt n$; "the two metrics dominate each other" and so boundedness is biconditional Referenced by: