Preservation of the Borel class under open-LC functions
نویسندگان
چکیده
منابع مشابه
Decomposing Borel Sets and Functions and the Structure of Baire Class 1 Functions
All spaces considered are metric separable and are denoted usually by the letters X, Y , or Z. ω stands for the set of all natural numbers. If a metric separable space is additionally complete, we call it Polish; if it is a continuous image of ω or, equivalently, of a Polish space, it is called Souslin. The main subject of the present paper is the structure of Baire class 1 functions. Recent de...
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For each a ∈ ω, we define a Baire class one function fa : ω → ω which encodes a in a certain sense. We show that for each Borel g : ω → ω, fa ∩ g = ∅ implies a ∈ ∆1(c) where c is any code for g. We generalize this theorem for g in a larger pointclass Γ. Specifically, when Γ = ∆2, a ∈ L[c]. Also for all n ∈ ω, when Γ = ∆3+n, a ∈M1+n(c).
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The following two theorems give the flavour of what will be proved. THEOREM. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0, 1] to Y coincide if and only if Y is connected and locally connected. THEOREM. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class fun...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2011
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm213-2-4