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On sequentially Ramsey sets

100%

Brzeska A.

Colloquium Mathematicum

2013

tom 131

nr 1

141-148

We consider sequentially completely Ramsey and sequentially nowhere Ramsey sets on $ω^ω$ with the topology generated by a free filter ℱ on ω. We prove that if ℱ is an ultrafilter, then the σ-algebra of Baire sets is the σ-algebra $S_{ℱ}𝓒𝓡$ of sequentially completely Ramsey sets. Further we study additivity and cofinality of the σ-ideal $S_{ℱ}𝓒𝓡 ⁰$ of sequentially nowhere Ramsey sets. We prove that if ℱ is a P(𝔟)-ultrafilter then $add(S_{ℱ}𝓒𝓡⁰) = 𝔟$, and if ℱ is a P-ultrafilter then $cof(S_{ℱ}𝓒𝓡⁰)$ is the point π-character of the space Seq(ℱ)$.

$P_{λ}$-sets and skeletal mappings

63%

Błaszczyk A., Brzeska A.

Colloquium Mathematicum

2013

tom 131

nr 1

89-98

We prove that if the topology on the set Seq of all finite sequences of natural numbers is determined by $P_λ$-filters and λ ≤ 𝔟, then Seq is a $P_λ$-set in its Čech-Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Brzeska A.

1 Błaszczyk A.

2 2013

Wyniki wyszukiwania

On sequentially Ramsey sets

$P_{λ}$-sets and skeletal mappings