On spaces with the ideal convergence property

• Autorzy: Jakub Jasinski , Ireneusz Recław
• Języki publikacji: EN

Abstrakty

EN

Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted 𝓘𝓒(I). We show that if I is an analytic, non-countably generated P-ideal then 𝓘𝓒(I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to $I_{b}$, then 𝓘𝓒(I) spaces have measure zero. We also present a characterization of the 𝓘𝓒(I) spaces using clopen covers.

Kategorie tematyczne

• 40A30: Convergence and divergence of series and sequences of functions
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 54C30: Real-valued functions
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 111
• Numer: 1
• Strony: 43-50

Daty

wydano

2008

Twórcy

autor

Jakub Jasinski

• Mathematics Department, University of Scranton, Scranton, PA 18510-4666, U.S.A.

autor

Ireneusz Recław

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/cm111-1-4