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there is no mapping $\\Phi:\\mathcal{S}_\\alpha\\to X$ for which $$ cd_{\\infty,\\alpha}(A,B)\\le \\|\\Phi(A)-\\Phi(B)\\|\\le C d_{1,\\alpha}(A,B) \\text{ for all $A,B\\in\\mathcal{S}_\\alpha$.}$$ Secondly, we prove for separable and reflexive Banach spaces $X$, and certain countable ordinals $\\alpha$ that $\\max(\\text{ 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