Timeline for An example of a $T_1$ space where all closed $G_\delta$ sets are zero-sets, but it isn't normal
Current License: CC BY-SA 4.0
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| Jun 12, 2021 at 14:07 | comment | added | Joseph Van Name | Recall that a P-space is a regular space where every $G_{\delta}$-set is open (every regular P-space is automatically zero-dimensional and hence completely regular). In a P-space, every closed $G_{\delta}$-set will be clopen and hence a zero set. There are certainly examples of P-spaces that are not normal (you can generalize the Tychonoff plank example to get a P-space). | |
| Jun 11, 2021 at 19:53 | vote | accept | Erekle Khurodze | ||
| Jun 11, 2021 at 14:56 | history | answered | Joseph Van Name | CC BY-SA 4.0 |