Timeline for non-maximal prime ideal in the ring of continuous functions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 10, 2011 at 12:06 | vote | accept | Hugo Chapdelaine | ||
| Dec 9, 2011 at 18:50 | comment | added | François G. Dorais | (Of course, I meant the sets $((1-1/n)/2,1/2)\cup(1/2,(1+1/n)/2)$.) | |
| Dec 9, 2011 at 18:45 | comment | added | François G. Dorais | @a-fortiori: Extend the filter generated by the sets $((1-1/n)/2,0)\cup(0,(1+1/n)/2)$ to an ultrafilter $U$. Note that that if $f \in m_U$ then $f(1/2) = 0$ by continuity, but $m_U$ is not the ideal of all functions that vanish at $1/2$ since $f(x) = x-1/2$ is not in $m_U$. | |
| Dec 9, 2011 at 17:28 | comment | added | user2035 | Could you please indicate how to construct an ultrafilter belonging to a non-maximal prime ideal (or show its existence)? | |
| Dec 9, 2011 at 16:33 | history | answered | Goldstern | CC BY-SA 3.0 |