View source for Talk:Paving

==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.  [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 19:17, 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)
: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)