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Feb 8, 2019 at 16:13 answer added Dap timeline score: 3
Feb 8, 2019 at 12:54 history edited Misha
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Feb 8, 2019 at 12:53 comment added Misha @erz: I do not have an example although I suspect that a totally disconnected subset of $R^2$ of positive area would give such an example.
Feb 8, 2019 at 12:27 history edited Misha CC BY-SA 4.0
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Feb 8, 2019 at 12:25 comment added Misha @YCor: Yes, even this case is unclear although I may have an argument in the 2-dimensional case (it was studied by people in robotics and I think their robot-navigation algorithm yields a positive answer).
Feb 8, 2019 at 5:04 comment added YCor What if $K$ is a Cantor space? even $n=2$ (where $K$ has to be topologically trivial) sounds not obvious to me.
Feb 8, 2019 at 5:03 history edited YCor CC BY-SA 4.0
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Feb 8, 2019 at 4:02 comment added erz What are the examples of the length metric space $X$ and $K\subset X$ - compact that does not locally separate $X$, such that the length metric on $X\backslash K$ is different from the subspace metric?
Feb 8, 2019 at 1:15 history asked Misha CC BY-SA 4.0