Timeline for About the finished, $\aleph_0$...-compactness
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Oct 16, 2019 at 15:53 | comment | added | YCor | Indeed, it seems that the definition of Lindelöf number is very bad and should be repaired... | |
| Oct 16, 2019 at 14:11 | comment | added | Robert Furber | @YCor I myself also prefer to use strict inequalities whenever cardinals come up, for this exact reason. However, it appears that the other definition is standard when defining the Lindelöf number (or at least was standard, back in the 80s when the Handbook of Set Theoretic Topology came out). | |
| Oct 16, 2019 at 13:39 | comment | added | YCor | Anyway, the $\le$-definition misses such a notion as "every cover has a subcover of cardinal $<\aleph_\lambda$" for each limit ordinal $\lambda$. | |
| Oct 16, 2019 at 13:01 | vote | accept | Dattier | ||
| Oct 16, 2019 at 12:31 | answer | added | Robert Furber | timeline score: 3 | |
| Oct 16, 2019 at 11:39 | comment | added | Dattier | ***SB theorem :***$(E,d)$ is separable iff (for all $A \subset E$ and card$(A)>$card$(\mathbb N)$ then $A$ have an accumulation point). | |
| Oct 16, 2019 at 11:35 | comment | added | Dattier | Do you known the super Bolzano theorem ? @ToddEisworth | |
| Oct 16, 2019 at 11:33 | comment | added | Todd Eisworth | If I understand your question correctly, these concepts are well-known in the set-theoretic topology community, usually phrased with terminology like, e.g., "Initially $\omega$-compact" (= countably compact) or "finally $\omega_1$-compact" (=Lindelof). The Handbook of Set-Theoretic Topology is a good source, even if it is 35 years old! | |
| Oct 16, 2019 at 10:49 | history | edited | Dattier | CC BY-SA 4.0 |
deleted 3 characters in body; edited title
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| Oct 16, 2019 at 10:44 | comment | added | Dattier | Yes $\mathbb N$-compact is a classical compact, with a $\alpha$-compact we can extract a subcover of cardinal $\leq \alpha$, so $\aleph_0$-compact is the seperable space for (E,d) metric fr.wikipedia.org/wiki/Espace_séparable | |
| Oct 16, 2019 at 10:26 | comment | added | YCor | Last and not least, the question is way too vague. | |
| Oct 16, 2019 at 10:25 | comment | added | YCor | Why do you call $\mathbb{N}$-compact what everybody calls "compact". Especially meaning distinct things for $\mathbb{N}$-compact and $\aleph_0$-compact is confusing. Actually, defining $\alpha$-compact as the condition that from every covering there exists a subcover of cardinal $<\alpha$ (rather than $\le\alpha$) gives a more general definition, for which $\aleph_0$-compact just means compact. | |
| Oct 16, 2019 at 10:22 | history | edited | YCor | CC BY-SA 4.0 |
fixed English
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| Oct 16, 2019 at 10:14 | history | asked | Dattier | CC BY-SA 4.0 |