Timeline for Is the reals the smallest connected ordered topological ring?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 9 at 19:36 | comment | added | Emil Jeřábek | If you fix $0<u\in H$, then for any $x$, $x\in H\implies(x-u,x+u)\subseteq H$ and $x\notin H\implies(x-u,x+u)\cap H=\varnothing$. | |
| Feb 9 at 19:08 | comment | added | Jeyrome Sapin | "$H = \{b:\exists n\in\mathbb N\,(-na\le b\le na)\}$ is a nontrivial convex subgroup, hence clopen". Here, does convex mean that $\forall x,y \in G : (0 \leq x \leq y) \wedge (y \in H) \Rightarrow x \in H$? How does this imply that $H$ is clopen for, I suppose, the order topology? | |
| Aug 27, 2014 at 14:05 | history | answered | Emil Jeřábek | CC BY-SA 3.0 |