Timeline for Sets and their characteristic functions
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 12, 2022 at 23:01 | comment | added | Christian Remling | @EmilJeřábek: This is actually a nicer way of stating the condition. | |
| Nov 12, 2022 at 22:47 | comment | added | Emil Jeřábek | @ChristianRemling Or equivalently, $\operatorname{int}\overline A\subseteq A\subseteq\overline{\operatorname{int}A}$. | |
| Nov 12, 2022 at 22:10 | comment | added | Gro-Tsen | Along similar lines: a set is regular open iff its characteristic function is normal lower semicontinuous (meaning that $f(x) = \operatorname{lim.sup}_{y\to x} \operatorname{lim.inf}_{z\to y} f(z)$). | |
| Nov 12, 2022 at 21:48 | comment | added | Christian Remling | $\chi_A$ quasi-continuous is (obviously) equivalent to both $A$ and $A^c$ having dense open subsets, and I'm not sure if there is a better way of saying this. | |
| Nov 12, 2022 at 20:30 | comment | added | Joel David Hamkins | Why do you need both $\epsilon$ and $\delta$? Isn't it equivalent to take $\epsilon=\delta$? Replace each with the minimum... | |
| Nov 12, 2022 at 20:23 | history | asked | Sam Sanders | CC BY-SA 4.0 |