Topology Proceedings 33 (2009), pp. 361-380

Theorems with uniform conditions on sets not belonging to algebras

L.Š. Grinblat

Let {A_l}_{l ∈ L} be a family of s-algebras on a set X, where |L| = ℵ₀, with A_l ≠ P(X) for any l ∈ L, and for any finite set J ⊂ L, where |J| = h ≥ 3, there exist 2h-2 pairwise disjoint sets belonging to P(X) \∩_{l ∈ J}A_l; then ∪_{l ∈ L} A_l ≠ P(X). If we substitute the estimate 2h-3 for 2h-2, this theorem does not hold.

Keywords: algebra on a set, ultrafilter, a set not belonging to algebras, pairwise disjoint sets, systems of distinct representatives

Mathematics Subject Classification: 03E05 (54D35)

Document formats: PDF file 219.5 Kb

Topology Proceedings, Volume 33 (2009)
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