Is there a compact normed real space which contains more than one element?
Im trying to grab some intuition on this subject. Would love to get some intuition if possible.
2026-04-06 07:33:32.1775460812
Compact normed real - spaces.
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No, there is not. Such a space would have a vector $v\ne0$, and then the sequence $(nv)_{n\in\Bbb N}$ would have no convergent subsequence (since $\lim_{n\to\infty}\|nv\|=\infty$). So, the space is not compact.