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Jun 3, 2023 at 9:56 comment added Mike_Bool Thanks Denis. What about the contrary? Can one conclude from $d_g\sim d_h$ on $A$ that $g\sim h$ on $A$, if $A$ is nice enough?
Jun 3, 2023 at 6:06 history edited YCor CC BY-SA 4.0
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Jun 3, 2023 at 3:48 history edited Mike_Bool CC BY-SA 4.0
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Jun 2, 2023 at 23:17 comment added Denis T If A is compact, it's trivially true. If A is not compact, and by "metric function" you mean induced metric and not inner one, it's not true; consider a plane with one metric being flat, and other obtained by multiplying flat metric by something like $\frac{cosh(x)}{cosh(y)}$, and take as $A$ small nbhd of x axis.
Jun 2, 2023 at 22:28 history edited Mike_Bool CC BY-SA 4.0
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Jun 2, 2023 at 22:27 history edited Mike_Bool CC BY-SA 4.0
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S Jun 2, 2023 at 22:26 review First questions
Jun 3, 2023 at 0:32
S Jun 2, 2023 at 22:26 history asked Mike_Bool CC BY-SA 4.0