Negligible subsets of the generalized Baire space ω_1^ω_1
نویسندگان
چکیده
منابع مشابه
Compact subsets of the Baire space
Let P be the natural forcing for producing a finite splitting tree using finite conditions. Namely, p ∈ P iff p ⊆ ω is a finite subtree and p ≤ q iff p ⊇ q is an end extension of q. End extension means if s ∈ p\q then s ⊇ t for some t ∈ q which is terminal in q, i.e., has no extensions in q. This order is countable and hence forcing equivalent to adding a single Cohen real. The union of P-gener...
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Our motivation for the study of negligible subsets is that, for a compact piecewise linear n-manifold M, it has been a long standing problem as to whether the space of homeomorphisms H(M) is an absolute neighborhood retract (The Homeomorphism Group Problem). It turns out ([GH]) that there is a dense Gδ subset G ⊂ H(M) which is homeomorphic to a s-manifold, where s is the countable infinite prod...
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One of the main goals of computable analysis is that of formalizing the complexity of theorems from real analysis. In this setting Weihrauch reductions play the role that Turing reductions do in standard computability theory. Via coding, we can transfer computability and topological results from the Baire space ω to any space of cardinality 2א0 , so that e.g. functions over R can be coded as fu...
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Perhaps the earliest results about pointwise compact sets of Baire class-1 functions are the two selection theorems of E. Helly found in most of the standard texts on real variable (see, e.g., [Lo], [N]). These two theorems are really theorems about a particular example of a compact set of Baire class-1 functions known today as Helly space, the space of all nondecreasing functions from the unit...
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We construct two Borel equivalence relations on the generalized Baire space κ, κ = κ > ω, with the property that neither of them is Borel reducible to the other. A small modification of the construction shows that the straightforward generalization of the Glimm-Effros dichotomy fails. By λ we denote the set of all functions κ→ λ. We define a topology to (λ) by letting the sets N(η1...,ηn) = {(f...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum fennicae Mathematica Dissertationes
سال: 1996
ISSN: 1239-6303,1798-2375
DOI: 10.5186/aasfmd.1996.107