Timeline for Subsets of $\mathbb{R}$, every nonempty subset of which generates a disconnected translation-invariant topology
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6, 2021 at 18:20 | vote | accept | Mike Krebs | ||
| Aug 5, 2021 at 7:58 | comment | added | YCor | @KPHart thanks for clarifying | |
| Aug 5, 2021 at 7:50 | comment | added | KP Hart | @YCor The question was: what if every subset generates a disconnected topology? In your $S$ the subset $(0,1)$ gives us the standard topology. | |
| Aug 4, 2021 at 10:30 | answer | added | KP Hart | timeline score: 3 | |
| Aug 4, 2021 at 9:50 | comment | added | YCor | If $S=[0,1]\cup\bigcup_{n\in\mathbf{Z}}[4n+2,4n+3]$, don't you get the discrete topology? (intersecting $S$ and $S+1$ yields $\{0\}$, and 4 translates of $S$ cover the line). | |
| Aug 3, 2021 at 17:58 | history | asked | Mike Krebs | CC BY-SA 4.0 |