In a normed ($\ell_q, 1 \leq q$ ) linear finite dimensional space $\mathbb R^n$, does bounded means totally bounded? What other hypothesis do I need here?
2026-03-25 15:59:06.1774454346
In finite dimensional space, bounded means totally bounded?
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You'll need additional hypotheses. An infinite set with the discrete metric is bounded but not totally bounded. Did you have some constraint on the metric in mind?