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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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homogenuity of $\ell^p$

I want to know the following: If $x_1, x_2, \cdots, x_n, y_1,y_2, \cdots, y_n \in \ell_p$ satisfies $\|x_i-x_j\|_p=\|y_i-y_j\|_p$ for any $i,j$, then does there exist isometry $F$ of $\ell_p$ which …
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