Timeline for Changing a metric to that 2 points have different distance
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2023 at 4:39 | answer | added | Saúl RM | timeline score: 1 | |
| Mar 17, 2023 at 4:26 | comment | added | D.S. Lipham | By the way, it seems intuitively true. Picture the space in the Hilbert cube (or for practical purposes, in $\mathbb R ^3$). Bend/stretch the space so that $x$ is closer to the middle, and $y$ is at the outside with a third point stretched far away from it. Then consider the bent space in the Euclidean metric. | |
| Mar 17, 2023 at 4:24 | history | edited | D.S. Lipham | CC BY-SA 4.0 |
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| Mar 17, 2023 at 4:23 | comment | added | D.S. Lipham | Yes, any metric that induces the same topology. | |
| Mar 17, 2023 at 4:22 | comment | added | Piotr Hajlasz | Do you mean $d'$ is topologically equivalent to $d$? You did not say that. Without that assumption your question is somewhat empty. | |
| Mar 17, 2023 at 4:03 | history | edited | D.S. Lipham | CC BY-SA 4.0 |
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| Mar 17, 2023 at 4:02 | comment | added | D.S. Lipham | I was thinking of connected spaces with more than 1 point. (edits made) | |
| Mar 17, 2023 at 3:49 | comment | added | Sam Hopkins | Trivial comment: not if $X$ has only two points :) | |
| Mar 17, 2023 at 3:46 | history | asked | D.S. Lipham | CC BY-SA 4.0 |