Smooth sets for a Borel equivalence relation
نویسندگان
چکیده
منابع مشابه
Smooth Sets for a Borel Equivalence Relation
We study some properties of smooth Borel sets with respect to a Borel equivalence relation, showing some analogies with the collection of countable sets from a descriptive set theoretic point of view. We found what can be seen as an analog of the hyperarithmetic points in the context of smooth sets. We generalize a theorem of Weiss from Z-actions to actions by arbitrary countable groups. We sho...
متن کاملSmooth Sets for Borel Equivalence Relation
We study some properties of smooth Borel set with respect to a Borel equivalence relation, showing some analogies with the collection of countable sets from a descriptive set theoretic point of view. We found what can be seen as an analog of the hyperaritmectic reals in the context of smooth sets. We also present some results about the σ-ideal of closed smooth sets.
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We propose a novel enhancement to the task of collision-testing a set of local paths. Our approach circumvents expensive collision-tests, yet it declares a continuum of paths collision-free by exploiting both the structure of paths and the outcome of previous tests. We define a homotopy-like equivalence relation among local paths and provide algorithms to (1) classify paths based on equivalence...
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ing from the proof given above for Gaboriau-Popa we obtain theorems such as: Theorem 2.10 Let (X, d) be a complete, separable metric space equipped with an atomless Borel probability measure μ. Suppose Γ acts ergodically by measure preserving transformations on (X,μ) and the action on (X, d) is expansive. Let (Et)0<t<1 be a collection of distinct countable Borel equivalence relations on X with:...
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The transitive closure of a reflexive, symmetric, analytic relation is an analytic equivalence relation. Does some smaller class contain the transitive closure of every reflexive, symmetric, closed relation? An essentially negative answer is provided here. Every analytic equivalence relation on an arbitrary Polish space is Borel embeddable in the transitive closure of the union of two smooth Bo...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1995-1303127-8