Timeline for A topological tree is weakly contractible
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2022 at 13:53 | comment | added | Cosine | @IlyaBogdanov : I think a real tree is always a metric space by definition, so e.g. the Long Line would not be a real tree, but it would a "topological tree" by my definition. | |
| Dec 20, 2022 at 11:51 | comment | added | Ilya Bogdanov | It seems that the alternative definition says your objects are real trees, see en.wikipedia.org/wiki/Real_tree | |
| Dec 19, 2022 at 17:00 | history | became hot network question | |||
| Dec 19, 2022 at 15:04 | vote | accept | Cosine | ||
| Dec 19, 2022 at 14:21 | answer | added | Jeremy Brazas | timeline score: 8 | |
| Dec 19, 2022 at 13:04 | comment | added | Cosine | @PierrePC: This is a very nice observation! Now that I think about it: It should even be possible to reduce the question to compact metrizable spaces as the continuous image of compact metrizable space inside a Hasdorff space is metrizable. | |
| Dec 19, 2022 at 10:40 | comment | added | Zerox | @Z.M The poster wrote pathwise connectedness, not pairwise connectedness. | |
| Dec 19, 2022 at 10:14 | comment | added | Z. M | I am not sure that your two definitions are equivalent, unless I misunderstood your "pairwise connectedness": the first implies that the space is path-connected, while the sencond does not seem to be so, e.g. the topologist's sine curve. | |
| Dec 19, 2022 at 9:30 | comment | added | Pierre PC | It seems to me that your question reduces to the case of compact Hausdorff spaces, since the image of any map from a sphere to a topological tree should be a compact Hausdorff topological tree. It is clearly Hausdorff, path connected, and compact. That we can find nice paths follows from the answer to your "hard question" for existence, and the tree property of the whole space for uniqueness. | |
| Dec 19, 2022 at 8:58 | history | asked | Cosine | CC BY-SA 4.0 |