Timeline for A topological concept dual to compactness
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2021 at 13:32 | history | edited | Paul Taylor |
added newly created tag
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| Nov 13, 2017 at 10:32 | answer | added | Christopher Townsend | timeline score: 0 | |
| Mar 9, 2015 at 1:46 | answer | added | Joseph Van Name | timeline score: 1 | |
| Jun 30, 2014 at 11:35 | answer | added | Paul Taylor | timeline score: 16 | |
| May 16, 2014 at 2:45 | answer | added | Joseph Van Name | timeline score: 3 | |
| May 5, 2014 at 14:15 | comment | added | Martin Argerami | @AliTaghavi: if $X$ is not Hausdorff, then $C(X) $ does not detect the topology of $X$. | |
| May 5, 2014 at 3:17 | comment | added | Jonathan Beardsley | @ToddTrimble Yeah, I find a lot of this stuff interesting and informative as well. | |
| May 5, 2014 at 3:01 | comment | added | Todd Trimble | @JonBeardsley The "froth" generated by Andrej is genuinely interesting and informative, and I think perhaps you underestimate people's "abilities". (François did in fact address the question as asked.) | |
| May 5, 2014 at 2:48 | comment | added | Jonathan Beardsley | This question gets an upvote because of all the froth it's generating, and because of people's general inability to just answer the question. =P | |
| May 5, 2014 at 0:54 | comment | added | Joseph Van Name | Let's define the anti-compactness number of a space $X$ to be the smallest cardinal $\lambda$ such that every closed cover of $X$ has a subcover of cardinality less than $\lambda$. Then the anti-compactness number of a Hausdorff space is the least cardinal above its cardinality. However, the anti-compactness number of a space can be generalized to point-free topology. Therefore, the anti-compactness number seems to be a point-free generalization of the notion of the cardinality of a topological space. | |
| May 4, 2014 at 19:36 | answer | added | François G. Dorais | timeline score: 4 | |
| May 4, 2014 at 13:28 | comment | added | François G. Dorais | At the risk of adding one more distracting terminological comment, let me point out that a space $X$ where every subset is 'anti-compact' in your sense is quite reasonably the dual idea of a Noetherian space. Though this would follow a nearly systematic naming tradition, I do not recommend calling such spaces 'Artinian spaces'! | |
| May 4, 2014 at 11:59 | comment | added | Henno Brandsma | anti-compact as a property name is already taken: $X$ anti-compact means that the only compact subsets of $X$ are the finite ones. E.g. a co-countable space is an example. | |
| May 4, 2014 at 10:05 | comment | added | Martin Sleziak | Similar question at MSE: Terminologies related to “compact?”. Some authors call spaces such that every closed cover has a finite subcover strongly S-closed. Some equivalent conditions are listed in my question here. (Sorry for the self-promotion, but link seemed better solution than posting the same list again here in a comment or an answer.) | |
| May 4, 2014 at 9:59 | answer | added | Andrej Bauer | timeline score: 65 | |
| May 4, 2014 at 9:38 | answer | added | Alexis Hazell | timeline score: 4 | |
| May 4, 2014 at 9:27 | comment | added | Martin Brandenburg | This is not really a natural definition of dual compactness ... | |
| S May 4, 2014 at 9:12 | history | suggested | Ali Taghavi |
I added a new tag
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| May 4, 2014 at 9:09 | review | Suggested edits | |||
| S May 4, 2014 at 9:12 | |||||
| May 4, 2014 at 9:07 | comment | added | Ali Taghavi | some particular questions arising from your question: Is the product of anti-compact space, anti-compact?what can be said about the continuous image of an anti compact space? assume that $X$ is a non Hausdorff compact space. Then $A=C(X)$, the algebra of all continuous complex functions on $X$, is a $C^{*}$ algebra. Now the question is that"what is an algebraic language for anti compactness, in term of $C^{*}$ algebras and non commutative topology? | |
| May 4, 2014 at 9:02 | review | First posts | |||
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| May 4, 2014 at 8:45 | history | asked | p modabberi | CC BY-SA 3.0 |