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1
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On the Separation Dimension of $K_ω$

100%
Hattori Y., van Mill J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2013
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tom 61
|
nr 1
67-70
EN
We prove that $trt K_ω > ω+1$, where trt stands for the transfinite extension of Steinke's separation dimension. This answers a question of Chatyrko and Hattori.
2
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Infinite-Dimensionality modulo Absolute Borel Classes

100%
Chatyrko V., Hattori Y.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2008
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tom 56
|
nr 2
163-176
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.
3
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On a question of de Groot and Nishiura

100%
Chatyrko V., Hattori Y.
Fundamenta Mathematicae
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2002
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tom 172
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nr 2
107-115
EN
Let $Zₙ = [0,1]^{n+1} ∖ (0,1)ⁿ × {0}$. Then cmp Zₙ < def Zₙ for n ≥ 5. This is the answer to a question posed by de Groot and Nishiura [GN] for n ≥ 5.
4
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Dugundji extenders and retracts on generalized ordered spaces

81%
Gruenhage G., Hattori Y., Ohta H.
Fundamenta Mathematicae
|
1998
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tom 158
|
nr 2
147-164
EN
For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an $L_{ch}$-extender (resp. $L_{cch}$-extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X\A; (iii) there is a continuous $L_{ch}$-extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and the pointwise convergence topology, for each space Y; (iv) A × Y is C*-embedded in X × Y for each space Y; (v) there is a continuous linear extender $φ:C*_{k}(A) → C_{p}(X)$; (vi) there is an $L_{ch}$-extender φ:C(A) → C(X); and (vii) there is an $L_{cch}$-extender φ:C(A) → C(X). We prove that these conditions are related as follows: (i)⇒(ii)⇔(iii)⇔(iv)⇔(v)⇒(vi)⇒(vii). If A is paracompact and the cellularity of A is nonmeasurable, then (ii)-(vii) are equivalent. If there is no connected subset of X which meets distinct convex components of A, then (ii) implies (i). We show that van Douwen's example of a separable GO-space satisfies none of the above conditions, which answers questions of Heath-Lutzer [9], van Douwen [1] and Hattori [8].
5
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On characterizations of classes of metrizable spaces that have transfinite dimension

79%
Hattori Y.
Fundamenta Mathematicae
|
1987
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tom 128
|
nr 1
37-46
6
Content available remote

On special metrics characterizing topological properties

60%
Hattori Y.
Fundamenta Mathematicae
|
1985-1986
|
tom 126
|
nr 2
133-145
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