Timeline for Is it possible to connect every compact set?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2020 at 4:33 | comment | added | erz | I think understand how to do that, but I decided to present the theorem I referred to (which is not hard by the way), since I was going to post a complement to your answer with a more detailed explanation. | |
| May 5, 2020 at 19:23 | comment | added | Anton Petrunin | @erz, yes, it can be done this way, but this theorem is hard (and I do not know its proof). Instead one may directly apply existence of arbitrary small path connected neighborhood. | |
| May 5, 2020 at 7:00 | vote | accept | erz | ||
| May 5, 2020 at 6:55 | comment | added | erz | Do I understand correctly that the control of the diameters of the curves comes from the fact that any locally path connected metrizable space admits a metric such that every ball of diameter less than some fixed number is path connected? Or is there a simpler way? | |
| May 5, 2020 at 6:37 | comment | added | erz | @მამუკაჯიბლაძე local path connected + connected implies path connected: the path components are open and disjoint, and therefore there is just one such path component | |
| May 5, 2020 at 5:01 | comment | added | Anton Petrunin | @მამუკაჯიბლაძე X is assumed to be locally path connected (perhaps), likely one may do the same with a weaker assumption. | |
| May 5, 2020 at 4:50 | comment | added | მამუკა ჯიბლაძე | Why is it possible to connect $x$ to $y$? Are you assuming path connectedness of $X$? I think the assumption is connected but only locally path connected? | |
| May 5, 2020 at 4:16 | history | answered | Anton Petrunin | CC BY-SA 4.0 |