Timeline for Union of connected sets
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2015 at 5:39 | vote | accept | 4869 | ||
| May 6, 2015 at 5:39 | vote | accept | 4869 | ||
| May 6, 2015 at 5:39 | |||||
| May 6, 2015 at 5:39 | vote | accept | 4869 | ||
| May 6, 2015 at 5:39 | |||||
| May 5, 2015 at 14:31 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
removed irrelevant tag
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| May 5, 2015 at 13:47 | comment | added | Joel David Hamkins | @Hachino In that case, it works if and only if $I$ is a well-order, and I have edited my answer to explain it. | |
| May 5, 2015 at 12:18 | comment | added | Hachino | @JoelDavidHamkins : And if you drop the assumption when $\beta$ is the least element ? Like when you require $\left ( \bigcup_{k < n }A_k \right )\cap A_n\neq \emptyset$ for $n \geq 1$ instead of $n \geq 0$ ? (The whole family is $(A_n)_{n\in \mathbb{N}}$.) | |
| May 5, 2015 at 12:00 | comment | added | Joel David Hamkins | The hypothesis as stated is impossible for a well-ordered set, since if $\beta$ is the least element, then $\bigcup_{\alpha<\beta}A_\alpha$ is itself empty. | |
| May 5, 2015 at 11:27 | answer | added | Joel David Hamkins | timeline score: 6 | |
| May 5, 2015 at 11:16 | comment | added | 4869 | And the order on the index set should not be well-ordered,or it is obvious as the countable one. | |
| May 5, 2015 at 11:14 | comment | added | 4869 | It is an open problem. You can add some conditions | |
| May 5, 2015 at 10:12 | comment | added | Joonas Ilmavirta | Some details seem to be missing. Are the sets $A_\alpha$ subsets of a Euclidean (or another fixed topological) space? You seem to have an order on the index set, is it well-ordered or of some other special type? | |
| May 5, 2015 at 10:08 | review | First posts | |||
| May 5, 2015 at 10:12 | |||||
| May 5, 2015 at 10:06 | history | asked | 4869 | CC BY-SA 3.0 |