Timeline for Separability of the Stone space of a free sigma-algebra
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 28, 2019 at 7:02 | vote | accept | LJGC | ||
| Jun 27, 2019 at 16:14 | comment | added | Robert Furber | @YCor If you replace Borel by Baire, your statement is correct (and can be found in Halmos's book, for example). However, it is false with Borel if $E$ is uncountable - a singleton in $2^E$ is a Borel set that is not a Baire set. | |
| Feb 7, 2019 at 22:03 | comment | added | YCor | Given the free $\sigma$-algebra $A_E$ on $E$ with free generators $(x_t)_{t\in E}$, is it correct that mapping $A_E$ to $2^{2^E}$ by $x_t\mapsto \{Y\in 2^E:t\in Y\}$ induces an isomorphism from $A_E$ onto the $\sigma$-algebra of Borel subsets of the compact space $2^E$? Surjectivity is clear, I'm just not sure for injectivity. If it indeed holds, this is a pretty concrete description (from which the cellularity fact is obvious). | |
| Feb 5, 2019 at 20:25 | answer | added | Ramiro de la Vega | timeline score: 5 | |
| Feb 4, 2019 at 18:18 | history | asked | LJGC | CC BY-SA 4.0 |