Timeline for Connectedness of the complements of the connected subsets
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| May 9, 2015 at 17:48 | comment | added | Włodzimierz Holsztyński | Ouch! Dylan, thank you. Obviously, you've answered both question since the answer to the second one, under the circumstances, follows instantly from yours. My initial reflex was that spaces with property (B) should be something like circle-like. I'll keep the previous version for the record, and may add a better version. | |
| May 9, 2015 at 17:40 | comment | added | Dylan Thurston | In fact, (E) also does not hold for topological graphs without endpoints. Consider the "dumbbell graph" $D$ formed by taking two vertices $x$ and $y$, joining them by an edge, and attaching loops at both $x$ and $y$. (This is a CW complex, and you can subdivide to make this a graph in some more strict sense.) Then $D \setminus \{x\}$ is not connected. | |
| May 9, 2015 at 17:37 | history | answered | Dylan Thurston | CC BY-SA 3.0 |