Timeline for A property for maps between metric spaces
Current License: CC BY-SA 4.0
18 events
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| Oct 19, 2023 at 14:35 | comment | added | Iosif Pinelis | @YCor : I think such a comment (which of course you are completely free to make now or at any other time) would have discouraged users (myself included) to some degree from answering this question. On the other hand, I have seen many questions of the same level of difficulty on MO left alone and sometimes generously upvoted, and recently I saw an answer (very generously upvoted), whose main idea was to use (non-rigorously) the approximation $e^x\approx1+x$ for small $x$. So, can we remove this thread (and then you could comment on the degree of difficulty of the question)? | |
| Oct 19, 2023 at 14:08 | comment | added | YCor | Yes, but I think that the question should be closed as off-topic and I'm not sure we agree on this. My main regret is not to have commented from the beginning something such as "There are trivial examples of non-isometries with this property (e.g. constant maps), and even non-similarities. Could you make the question a little more specific, or at least explain what are your thoughts so far?" | |
| Oct 19, 2023 at 12:18 | comment | added | Iosif Pinelis | @YCor : I am glad that, apparently, we have eventually agreed that there appears to be no reasonable way to interpret the original question other than literally or to modify it in a reasonable way. Of course, this takes us back to what was the point of your first (rather aggressively stated) comment in this thread (and I hope we can now avoid going around in circles). Simply speaking, I think all this thread should be removed. If you remove all your comments in this thread, I will remove all my comments here. | |
| Oct 19, 2023 at 11:20 | comment | added | YCor | My answer is then: none that I could have decided myself in the name of the OP. In any case the answer is accepted, so this discussion is now pointless. | |
| Oct 19, 2023 at 11:11 | comment | added | Iosif Pinelis | @YCor : However, my question was "What could such a modification be?". | |
| Oct 18, 2023 at 22:03 | comment | added | YCor | Exactly, this is why I called it a follow-up question, and not a modification. | |
| Oct 18, 2023 at 18:47 | comment | added | Iosif Pinelis | @YCor : To me, this follow-up question seems to be a bit too far from the OP to be called a modification. | |
| Oct 18, 2023 at 14:25 | comment | added | YCor | A modification could be: just the same question, but mentioning the most trivial examples. Of course this makes the question quite open-ended. A specific follow-up question: what are spaces for which every self-map $f$ preserving this ternary relation is a similarity (i.e. multiplies the distance by a scalar)? Etc. | |
| Oct 18, 2023 at 14:16 | comment | added | Iosif Pinelis | @YCor : Then, I think, this is what you should have said right away. And then you could also have posted what you thought would be a potentially interesting modification of the question. I am actually curious: What could such a modification be? | |
| Oct 18, 2023 at 14:10 | comment | added | YCor | My general point is that off-topic questions are not worth answers. Your interpretation of the question is perfectly reasonable and this was the first I understood — and it is confirmed by the fact your answer is accepted. In a sense, I'm disappointed that a potentially interesting question is "settled" by a trivial remark. | |
| Oct 18, 2023 at 14:08 | comment | added | Iosif Pinelis | @YCor : If you would introduce (say $k$) properties in addition to the two properties in question, then you would be talking about relations between $k+2$ properties rather than between the original two properties. I think everyone is free to entertain such a modification of the literal reading of the question, but it is hardly reasonable to insist on that, as it now seems to be the case with your first comment to my question. | |
| Oct 18, 2023 at 13:37 | vote | accept | gm01 | ||
| Oct 18, 2023 at 4:27 | comment | added | YCor | In this interpretation, the question is highly off-topic: examples of non-isometries already occur between two 2-point metric spaces. When I say open-ended, I mean, for instance that when some condition are given on $X$ and $Y$, the question of determining such maps might become more interesting. E.g., what are spaces $X$ for which the only $f:X\to X$ with the condition are similarities (i.e., multiply the distance by a constant)? What about Euclidean spaces? | |
| Oct 18, 2023 at 1:33 | comment | added | Iosif Pinelis | @YCor : Why do you think the question " How is it related to $f$ being an isometry?" is quite open-ended? What kinds of relations can there be, in principle, between two properties? The only such relations that I can see are implications: that one of the properties implies (or does not imply) the other one. If the OP knew such relations, they should have been mentioned in the OP -- but then what would be the point of question "How is it related to $f$ being an isometry?"? So, I fail to see the point of your first comment to my question. | |
| Oct 17, 2023 at 22:43 | comment | added | YCor | I don't really know, OP's question is quite open-ended. | |
| Oct 17, 2023 at 21:01 | comment | added | Iosif Pinelis | @YCor : On the other hand, do you know what else can be said about this particular property -- especially concerning its relation with being an isometry? | |
| Oct 17, 2023 at 17:52 | comment | added | YCor | There are so many trivial examples of non-isometries with this property that I expect OP to be aware of them. | |
| Oct 17, 2023 at 17:26 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |