Timeline for Embedding ordinals with the order topology into connected $T_2$-spaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2018 at 5:57 | vote | accept | Dominic van der Zypen | ||
| Sep 20, 2018 at 20:15 | answer | added | KP Hart | timeline score: 7 | |
| Sep 20, 2018 at 20:00 | comment | added | Will Brian | @JamesHanson: That's correct. (You can prove it via transfinite induction. I don't have a reference, but I encourage you to give it a try -- it's a good exercise.) | |
| Sep 20, 2018 at 19:34 | comment | added | James E Hanson | I'm fairly sure every countable ordinal can be embedded in $\mathbb{R}$. | |
| Sep 20, 2018 at 19:06 | comment | added | Dominic van der Zypen | Good question @JamesHanson. Even if we take everyone's darling space $\mathbb{R}$ with the Euclidean topology, I think it is not hard to see that $\omega \cdot \omega$ can be embedded into $\mathbb{R}$, but I am not sure about larger limit ordinals. So I do not know the smallest ordinal that cannot be embedded into $\mathbb{R}$ even. But this is certainly known, I'll try and Google it | |
| Sep 20, 2018 at 17:14 | comment | added | James E Hanson | Do you know if every countable ordinal embeds into every non-trivial connected $T_2$ space? | |
| Sep 20, 2018 at 15:52 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
deleted 30 characters in body
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| Sep 20, 2018 at 15:24 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |