On the Borel class of the derived set operator. II
Douglas Cenzer, R. Daniel Mauldin (1983)
Bulletin de la Société Mathématique de France
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Douglas Cenzer, R. Daniel Mauldin (1983)
Bulletin de la Société Mathématique de France
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Alexey Ostrovsky (2011)
Fundamenta Mathematicae
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Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.
Costley, Charles G. (1972)
Portugaliae mathematica
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Michael Rice, George Reynolds (1980)
Fundamenta Mathematicae
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Lester E. Dubins, Karel Prikry (1995)
Séminaire de probabilités de Strasbourg
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Marcin Kuczma (1970)
Fundamenta Mathematicae
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Greg Hjorth, Alexander S. Kechris (2001)
Fundamenta Mathematicae
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Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible...
Roger Crocker (1969)
Colloquium Mathematicae
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I. Kátai (1977)
Colloquium Mathematicae
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W. Narkiewicz (1974)
Colloquium Mathematicae
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Alessandro Andretta, Donald A. Martin (2003)
Fundamenta Mathematicae
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Two sets of reals are Borel equivalent if one is the Borel pre-image of the other, and a Borel-Wadge degree is a collection of pairwise Borel equivalent subsets of ℝ. In this note we investigate the structure of Borel-Wadge degrees under the assumption of the Axiom of Determinacy.
Benjamin D. Miller (2007)
Fundamenta Mathematicae
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Answering a question of Kłopotowski, Nadkarni, Sarbadhikari, and Srivastava, we characterize the Borel sets S ⊆ X × Y with the property that every Borel function f: S → ℂ is of the form f(x,y) = u(x) + v(y), where u: X → ℂ and v: Y → ℂ are Borel.
R. Purves (1966)
Fundamenta Mathematicae
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