Embedding the cycle metric into a real vector space with metric $l_{p}$
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Why is it impossible to embed the cycle metric over $n$ points $x_{1}, x_{2},...,x_{n}$ where the distance is defined as the shortest path ($d(x_{i}, x_{j}) = min(|j-i|; n + i - j; n + j - i) $) into any real vector space equipped with the $l_{p}$ metric without incurring any nontrivial distortion?
metric-spaces
asked Nov 14 at 19:33
Ann He
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Why is it impossible to embed the cycle metric over $n$ points $x_{1}, x_{2},...,x_{n}$ where the distance is defined as the shortest path ($d(x_{i}, x_{j}) = min(|j-i|; n + i - j; n + j - i) $) into any real vector space equipped with the $l_{p}$ metric without incurring any nontrivial distortion?
metric-spaces
asked Nov 14 at 19:33
Ann He
165
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Why is it impossible to embed the cycle metric over $n$ points $x_{1}, x_{2},...,x_{n}$ where the distance is defined as the shortest path ($d(x_{i}, x_{j}) = min(|j-i|; n + i - j; n + j - i) $) into any real vector space equipped with the $l_{p}$ metric without incurring any nontrivial distortion?
metric-spaces
asked Nov 14 at 19:33
Ann He
165
Why is it impossible to embed the cycle metric over $n$ points $x_{1}, x_{2},...,x_{n}$ where the distance is defined as the shortest path ($d(x_{i}, x_{j}) = min(|j-i|; n + i - j; n + j - i) $) into any real vector space equipped with the $l_{p}$ metric without incurring any nontrivial distortion?
metric-spaces
metric-spaces
asked Nov 14 at 19:33
Ann He
165
asked Nov 14 at 19:33
Ann He
165
asked Nov 14 at 19:33
Ann He
165
asked Nov 14 at 19:33
Ann He
165
asked Nov 14 at 19:33
Ann He
165
165
add a comment |
add a comment |
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