Timeline for Convergence of distance
Current License: CC BY-SA 4.0
23 events
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| Mar 29 at 21:34 | comment | added | Star | Also, it must be that for $L_n=L>0$, $C_n(L)$ tends to a superset of $A$... This is by definition. | |
| Mar 29 at 21:26 | comment | added | Star | there is no rule on how many questions I can ask. You are free not to reply. | |
| Mar 29 at 21:22 | history | bounty ended | Star | ||
| Mar 29 at 21:22 | vote | accept | Star | ||
| Mar 29 at 20:25 | comment | added | Iosif Pinelis | Previous comment continued: Your additional requests keep ignoring that and concern things that cannot possibly make a substantial difference. | |
| Mar 29 at 20:23 | comment | added | Iosif Pinelis | @Star : No, I don' t think so. You actually seem to go in the wrong direction with the constant $L$. Anyhow, didn't we agree that, as your question had already been fully answered (along with a number of extra comments of mine), your last additional request was at Mar 25 at 18:30? Also, let me repeat: "I believe that all this pursuit, without serious structural restrictions on $\ell$ and $u$ (such as a seriously strong version of injectivity) is, unfortunately, fruitless. " | |
| Mar 29 at 20:14 | comment | added | Star | The Hausdorff distance, sorry. | |
| Mar 29 at 17:06 | comment | added | Iosif Pinelis | "the distance"? What distance? | |
| Mar 29 at 16:48 | comment | added | Star | Thanks. I think I'm OK with that. Am I right to say that if $L_n\equiv L>0$, then the distance goes to zero? | |
| Mar 27 at 1:26 | comment | added | Iosif Pinelis | @Star : Do you have a further response to this answer? | |
| Mar 26 at 0:16 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 26 at 0:10 | comment | added | Iosif Pinelis | @Star : This is now done. | |
| Mar 26 at 0:10 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 25 at 20:45 | comment | added | Star | Yes, please, thanks | |
| Mar 25 at 19:01 | comment | added | Iosif Pinelis | @Star : Since your question has already been fully answered (along with a number of extra comments of mine), I will do this modification (which, I believe, does not change anything of essence) if this is the last additional request. | |
| Mar 25 at 18:30 | comment | added | Star | If it is not a huge work, could you edit your answer along those lines? | |
| Mar 25 at 18:16 | comment | added | Iosif Pinelis | @Star : I did that in order for the counterexample to be simple and specific. However, the counterexample can be easily modified for any positive sequence $(L_n)$ converging to $0$ -- by then letting $p_n:=2L_n$, say. There are a huge number of degrees of freedom in constructing a counterexample under your conditions. | |
| Mar 25 at 17:55 | comment | added | Star | But it seems that you have picked a specific $L_n$? | |
| Mar 25 at 17:29 | comment | added | Iosif Pinelis | @Star : Essentially, this example shows that, for any positive sequence $(L_n)$ converging to $0$, we can construct $X,\ell,u,(p_n)$ with $d_H(A,C_n(L_n))$ however large or even infinite for all $n$. I believe that all this pursuit, without serious structural restrictions on $\ell$ and $u$ (such as a seriously strong version of injectivity) is, unfortunately, fruitless. | |
| Mar 25 at 17:05 | comment | added | Star | Thanks. Is your example showing that there is no $L_n$ that makes the claim true? | |
| Mar 25 at 15:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 25 at 14:48 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Mar 25 at 14:42 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |