Timeline for Requirement for connected sets
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16, 2019 at 0:04 | comment | added | Anton Petrunin | @KConrad, Note that $|x-a|=R$ for any $x\in \bar S\backslash S$, therefore $s\in S$. | |
| Mar 15, 2019 at 15:07 | comment | added | KConrad | Oh, so "$s \in S$" should be "$s \in \overline{S}$". Then my objection no longer applies. | |
| Mar 15, 2019 at 14:57 | comment | added | Christian Remling | @KConrad: I don't think this is being claimed: I interpret "the space" as the whole space, not $S$, though then the claim should be "... there is a point $s\in\overline{S}$ ..." Robert just posted the same argument with more details. | |
| Mar 15, 2019 at 10:01 | comment | added | KConrad | Why is $S$ compact (from which you know distance from $S$ to $a$ has a minimum)? A connected component of an open subset is closed in the open subset but need not be closed (hence compact) in the whole space, in general. | |
| Mar 15, 2019 at 3:39 | history | answered | Anton Petrunin | CC BY-SA 4.0 |