Timeline for Covering image of a connected CW-complex need not be a CW-complex
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2021 at 18:08 | history | undeleted | Sumanta | ||
| Feb 23, 2021 at 16:10 | history | deleted | Sumanta | via Vote | |
| Jan 14, 2021 at 18:56 | history | undeleted | Sumanta | ||
| Jan 14, 2021 at 14:10 | history | deleted | Sumanta | via Vote | |
| Jan 14, 2021 at 12:38 | history | undeleted | Sumanta | ||
| Jan 14, 2021 at 11:17 | history | deleted | Sumanta | via Vote | |
| Jan 14, 2021 at 6:13 | comment | added | mme | I think an example is given in Exercise 1.3.25 of Hatcher. There is a covering space action of Z on the punctured plane with non-Hausdorff orbit spaces (call it Y) with fundamental group Z^2. Any map from Y to a Hausdorff space factors through a Hausdorffizafion Haus(Y). This space Haus(Y) is homeomorphic to S^1 x X, where X = R sqcup_0 R (the literal letter X without its endpoints). This has fundamental group Z. Hence any map from Y to a CW complex induces a map on pi_1 with cyclic image; there is no CW complex Y' with f: Y -> Y' which is an isomorphism on pi_1, as Z^2 is not cyclic. | |
| Jan 14, 2021 at 4:19 | history | edited | Sumanta | CC BY-SA 4.0 |
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| Jan 13, 2021 at 17:31 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading (mostly missing spaces); deleted "thanks", per community norms
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| Jan 13, 2021 at 17:24 | history | edited | Sumanta | CC BY-SA 4.0 |
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| Jan 13, 2021 at 16:24 | comment | added | Moishe Kohan | If $Y$ is locally-compact then it will be a metrizable ANR, hence, homotopy-equivalent to a CW complex. | |
| Jan 13, 2021 at 16:14 | history | asked | Sumanta | CC BY-SA 4.0 |