Timeline for An example of a Borel map of the first class
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2018 at 0:32 | comment | added | YCor | A map from $X$ to $Y$ is denoted $X\to Y$. The symbol $\mapsto$ is used to denote the assignment $x\mapsto f(x)$, and precisely to distinguish it from the map itself. I edited accordingly. Also removed confusing use of minus sign, replaced by words. | |
| Jun 26, 2018 at 0:32 | history | edited | YCor | CC BY-SA 4.0 |
removed confusing notation and changed tags
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| Jun 8, 2018 at 10:29 | comment | added | Tony T. | Multivalued mapping $F:2^X \mapsto 2^Y$ has 2nd Borel class, for $f-$ 1st Borel class. So I think for G there exists a similar theorem, but I dont know it. For $\omega$ I used theorem 3.1 from M. M. Čoban, “Multi-valued mappings and Borel sets” | |
| Jun 8, 2018 at 10:12 | comment | added | Tony T. | I thougth, the Dirichlet function the example of 2nd Borel class,where $2^X\mapsto 2^Y$ and $2^Y\mapsto 2^X$ aren't Borel mappings. | |
| Jun 7, 2018 at 23:19 | review | Close votes | |||
| Jul 9, 2018 at 3:04 | |||||
| Jun 7, 2018 at 18:51 | comment | added | Andreas Blass | It's not clear what your $G$ and $\theta$ are intended to be. The only obvious map $2^Y\to2^X$ is inverse image under $f$, but that doesn't naturally factor through $X$. And the only obvious map $X\to2^X$ would be $x\mapsto\{x\}$, but your $\omega$ is apparently something else --- what is it? | |
| Jun 7, 2018 at 18:50 | comment | added | Taras Banakh | The composition of two maps of the 1-st Borel class needs not be of the first Borel class: the classical Dirichlet function (the characteristic function of rationals) can be written as a composition of two functions of the first Baire class. | |
| Jun 7, 2018 at 18:43 | history | asked | Tony T. | CC BY-SA 4.0 |