Timeline for Classification of 1-dimensional manifolds (not second-countable)
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2022 at 14:48 | comment | added | Jim Conant | Just a remark, but in addition to second countable, you also need to assume Hausdorff. Otherwise you get examples like the line with two origins. | |
| Apr 19, 2022 at 23:07 | history | edited | Lee Mosher | CC BY-SA 4.0 |
Fixed the wikipedia link
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| Sep 8, 2012 at 10:12 | vote | accept | Martin Brandenburg | ||
| Sep 8, 2012 at 7:11 | answer | added | Todd Trimble | timeline score: 17 | |
| Apr 17, 2010 at 17:46 | comment | added | Martin Brandenburg | @Qiaochu: there are non-isomorphic orders, whose order topologies are homeomorphic. @Robin: alright! | |
| Apr 17, 2010 at 17:17 | comment | added | Robin Chapman | Qiaochu, arguably a simpler way to see that the (1-sided) long ray is not homeomorphic to the (2-sided) long line is that removing a point from the former always creates one paracompact component, but removing a point from the latter never does. | |
| Apr 17, 2010 at 17:09 | comment | added | Qiaochu Yuan | As the Wikipedia article states, an increasing sequence in the long ray converges; this isn't true of a decreasing sequence, so the two ends behave differently. | |
| Apr 17, 2010 at 16:47 | history | edited | Martin Brandenburg | CC BY-SA 2.5 |
deleted 119 characters in body; added 61 characters in body
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| Apr 17, 2010 at 16:43 | comment | added | Gerald Edgar | Compact and first-countable implies second-countable, right? So if you try a "long circle" the point at infinity won't have a local neighborhood such as the one required for a "manifold". | |
| Apr 17, 2010 at 16:35 | history | edited | Robin Chapman | CC BY-SA 2.5 |
spelling correction
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| Apr 17, 2010 at 16:34 | comment | added | Alison Miller | I'm having trouble finding a reference for the long circle (it's not listed in the wikipedia entry, and I'm not sure how to interpret your last sentence). | |
| Apr 17, 2010 at 16:20 | history | asked | Martin Brandenburg | CC BY-SA 2.5 |