On sequentially Ramsey sets

• Autorzy: Anna Brzeska
• Języki publikacji: EN

Abstrakty

EN

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)$.

Kategorie tematyczne

• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 54D70: Base properties
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
• 54D80: Special constructions of spaces (spaces of ultrafilters, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 1
• Strony: 141-148

Daty

wydano

2013

Twórcy

autor

Anna Brzeska

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/cm131-1-12