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Infinite-Dimensionality modulo Absolute Borel Classes

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Chatyrko V., Hattori Y.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

tom 56

nr 2

163-176

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.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Chatyrko V.

1 Hattori Y.

1 2008

Wyniki wyszukiwania

Infinite-Dimensionality modulo Absolute Borel Classes