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Let X and Y be two spaces equipped respectively with two metrics [itex]d_1[/itex] and [itex]d_2[/itex], and let's consider a mapping [itex]f:(X,d_1)\rightarrow(Y,d_2)[/itex]

How can I formalize the fact that for any pointxin X, all the points that are"very close"tox(respect to the metric [itex]d_1[/itex]) must be mapped into points in Y that are "very close" tof(x)(with respect to the metric [itex]d_2[/itex]).

Thanks!

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# Question about relationship between metrics

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