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Difference between revisions of "Talk:Paving"

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(strange article)
(→‎Definition of compact: another source)
 
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:Surely not. Looking for instance at [http://www.ams.org/journals/proc/1978-069-01/S0002-9939-1978-0466469-X/S0002-9939-1978-0466469-X.pdf Alan Sultan 1978] I see that, first, a paving is required to be a lattice of subsets, and second, compactness is defined in a way equivalent to yours, not to one in our (strange) article. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:13, 14 October 2017 (CEST)
 
:Surely not. Looking for instance at [http://www.ams.org/journals/proc/1978-069-01/S0002-9939-1978-0466469-X/S0002-9939-1978-0466469-X.pdf Alan Sultan 1978] I see that, first, a paving is required to be a lattice of subsets, and second, compactness is defined in a way equivalent to yours, not to one in our (strange) article. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:13, 14 October 2017 (CEST)
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:Or [https://www.sciencedirect.com/science/article/pii/S0166864101002498 Alvarez-Manilla 2002]; here a paving is an ''arbitrary'' set of subsets, but compact paving is defined exactly as you did above. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:29, 14 October 2017 (CEST)

Latest revision as of 18:29, 14 October 2017

Definition of compact

The definition of compactness in terms of the finite intersection property here seems wrong. The text says

A compact paving is a paving $\mathcal{C}$ with the FIP: for every finite subset $\{C_1,\ldots,C_n\} \subset \mathcal{C}$, $\cap_{i=1}^n C_i \ne \emptyset$.

The reference says that

any $\mathcal{F} \subset \mathcal{C}$ having the FIP has non-empty intersection

I don't think these are the same. Richard Pinch (talk) 19:17, 14 October 2017 (CEST)

Surely not. Looking for instance at Alan Sultan 1978 I see that, first, a paving is required to be a lattice of subsets, and second, compactness is defined in a way equivalent to yours, not to one in our (strange) article. Boris Tsirelson (talk) 20:13, 14 October 2017 (CEST)
Or Alvarez-Manilla 2002; here a paving is an arbitrary set of subsets, but compact paving is defined exactly as you did above. Boris Tsirelson (talk) 20:29, 14 October 2017 (CEST)
How to Cite This Entry:
Paving. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Paving&oldid=42072