Infinite-Dimensionality modulo Absolute Borel Classes

• Autorzy: Vitalij Chatyrko , Yasunao Hattori
• Języki publikacji: EN

Abstrakty

EN

For each ordinal 1 ≤ α < ω₁ we present separable metrizable spaces $X_α$, $Y_α$ and $Z_α$ such that
(i) $fX_α, fY_α, fZ_α = ω₀$, where f is either trdef or 𝓚₀-trsur,
(ii) $A(α)-trind X_α = ∞$ and $M(α)-trind X_α = -1$,
(iii) $A(α)-trind Y_α = -1$ and $M(α)-trind Y_α = ∞$, and
(iv) $A(α)-trind Z_α = M(α)-trind Z_α = ∞$ and $A(α+1) ∩ M(α+1)-trind Z_α = -1$.
We also show that there exists no separable metrizable space $W_α$ with $A(α)-trind W_α ≠ ∞$, $M(α)-trind W_α ≠ ∞$ and $A(α) ∩ M(α)-trind W_α = ∞$, where A(α) (resp. M(α)) is the absolutely additive (resp. multiplicative) Borel class.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 2
• Strony: 163-176

Daty

wydano

2008

Twórcy

autor

Vitalij Chatyrko

• Department of Mathematics, Linköping University, 581 83 Linköping, Sweden

autor

Yasunao Hattori

• Department of Mathematics, Shimane University, Matsue, 690-8504 Japan

Identyfikatory

DOI

10.4064/ba56-2-7