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Does there exist a compact normed linear space?

All I can see is that if there is any it must be finite-dimensional. But does there exist any other than the trivial one i.e. $(0)$?

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  • $\begingroup$ Is the real line or the complex line compact? $\endgroup$ – kimchi lover Feb 16 at 18:12
  • $\begingroup$ No @kimchilover.............. $\endgroup$ – Jave Feb 16 at 18:13
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    $\begingroup$ There you are, then: if there is a non-zero element of your space, it contains a copy of the scalar multiples of that element. $\endgroup$ – kimchi lover Feb 16 at 18:14
  • $\begingroup$ See here: math.stackexchange.com/questions/941897/… $\endgroup$ – Math1000 Feb 16 at 20:36

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