Timeline for On the existence of a sequence of positive continuous functions
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2022 at 22:47 | comment | added | Gerry Myerson | @Giorgio, thanks, I'll have a look. | |
| Apr 9, 2022 at 16:27 | comment | added | Giorgio Metafune | Here is the paper by Sierpinski I am referring to: W. Sierpinski, Sur l'ensemble des points de convergence d'une suite de fonctions continues, Fund. Math. 2(1921), 41-49. It was quoted in an answer by @Willie Wong which I am unable to find again. The paper is very general but specializing to the case of a countable set gives quite a simple construction of the sequence, without using Diophantine approximation. | |
| Apr 9, 2022 at 12:29 | comment | added | Gerry Myerson | @Giorgio, can you just post here the author, title, journal volume year pages? or a link to Willie Wong's post? | |
| Apr 9, 2022 at 9:49 | comment | added | Giorgio Metafune | Actually I got the paper from a later post answered from Willie Wong. I can send the paper to you, if you like to have it. | |
| Apr 9, 2022 at 9:29 | comment | added | Gerry Myerson | @Giorgio, good! Maybe you could write up what you found, and where you found it, and post it. | |
| Apr 9, 2022 at 6:43 | comment | added | Giorgio Metafune | Gerry, thank you for your answer. I just found an old paper by Sierpinki which is very clear (and avoids any number theory). | |
| Apr 9, 2022 at 5:02 | comment | added | Gerry Myerson | @Giorgio, maybe you should post this as a new question. | |
| Apr 8, 2022 at 13:15 | comment | added | Giorgio Metafune | I know that this is a very old post...but let me try asking. I do not see how to fill the details to get $f_n(x)=0$ for most $n$ in the last case. In principle having $|x-p/q| \leq q^{-4}$ does not prevent to have $|x-p/q| \leq n^{-4}$ for many $ n \geq q$ until we reach the next good approximation $r/s$. Could you give some more detail? | |
| Aug 30, 2010 at 13:25 | history | edited | Gerry Myerson | CC BY-SA 2.5 |
added 815 characters in body
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| Aug 3, 2010 at 23:24 | comment | added | Gerry Myerson | @Robin, I think I do remind you of the author. | |
| Aug 3, 2010 at 21:12 | comment | added | Robin Chapman | Can you remind us of the author please, Gerry? | |
| Aug 3, 2010 at 12:36 | history | answered | Gerry Myerson | CC BY-SA 2.5 |