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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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Ribe's Theorem: finitely representability between two uniformly homeomorphic Banach spaces

An infinite-dimensional Banach space $X$ is said to be crudely finitely representable (with constant $\lambda$) in an infinite-dimensional Banach space $Y$ if there is a constant $\lambda>1$ such that …