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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

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Radii and centers in Banach spaces

I believe that the property does not hold for all Banach spaces, but my counterexample is a little involved. If you've the patience then follow me through... Let $V=\bigoplus_{n=1}^\infty \ell^n_2$ …
J Bytheway's user avatar