Isometric Embeddings of Snowflakes into Finite-dimensional Banach Spaces
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چکیده
We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space X isometrically embeds into some finite-dimensional normed space if and only if X is finite. In the case of power functions we give a uniform bound on the cardinality of X depending only on the power exponent and the dimension of the vector space.
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تاریخ انتشار 2017