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maximum, , or Chebyshev distance is defined by) because if it was $then\; the\; fact\; that\; is\; a\; Banach\; space\; would\; imply\; that\; it\; converges\; (a\; contradiction).$

Equivalence of metrics

For a given set X, two metrics and are called topologically equivalent (uniformly equivalent) if the identity mapping
:is a homeomorphism (uniform isomorphism).

For example, if is a metric, then

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