Timeline for When is the weak topology generated by a family of functions Baire?
Current License: CC BY-SA 4.0
7 events
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| Jul 11, 2019 at 9:15 | comment | added | erz | I don't think assuming that $A$ is a C* algebra is essential actually, since a collection of functions generates the same topology as the collection of all possible C* combinations of them, and a collection generates the same topology as its closure in $C_b(X)$. | |
| Jul 9, 2019 at 20:42 | comment | added | Douglas Somerset | If you assume that $A$ is a C$^*$-algebra then $X/R$ will be the Gelfand space of $A$, where $R$ is the equivalence relation on $X$ consisting of points not separated by $A$. So $X/R$ will be locally compact and Baire, and hence $X$ will be too in the weak topology. | |
| Jul 9, 2019 at 19:03 | history | rollback | Merry |
Rollback to Revision 1
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| Jul 9, 2019 at 19:01 | comment | added | Merry | @DouglasSomerset It indeed is! | |
| Jul 8, 2019 at 22:38 | comment | added | Douglas Somerset | I think that the edit to the title is erroneous. | |
| Jun 7, 2019 at 5:55 | history | edited | user64494 | CC BY-SA 4.0 |
The title is improved.
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| Jun 6, 2019 at 23:22 | history | asked | Merry | CC BY-SA 4.0 |