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. 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)