[: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:__