منابع مشابه
Grey Subsets of Polish Spaces
We develop the basics of an analogue of descriptive set theory for functions on a Polish space X. We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric groups with ample generics have this property. We also extend classical theorems of Effros and Hausdorff to the topometric context.
متن کاملPacking Index of Subsets in Polish Groups
For a subset A of a Polish group G, we study the (almost) packing index indP (A) (resp. IndP (A)) of A, equal to the supremum of cardinalities |S| of subsets S ⊂ G such that the family of shifts {xA}x∈S is (almost) disjoint (in the sense that |xA ∩ yA| < |A| for any distinct points x, y ∈ S). Subsets A ⊂ G with small (almost) packing index are small in a geometric sense. We show that indP (A) ∈...
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We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π2 in the Borel hierarchy. ...
متن کاملNoetherian Quasi-Polish spaces
In the presence of suitable power spaces, compactness ofX can be characterized as the singleton {∅} being open in the space A(X). Equivalently, this means that universal quantification over a compact space preserves open predicates. Using the language of represented spaces, one can make sense of notions such as a Σ 2 subset of the space of Σ 2 -subsets of a given space. This suggests higher-ord...
متن کاملIsometry of Polish metric spaces
We consider the equivalence relation of isometry of separable, complete metric spaces, and show that any equivalence relation induced by a Borel action of a Polish group on a Polish space is Borel reducible to this isometry relation. We also consider the isometry relation restricted to various classes of metric spaces, and produce lower bounds for the complexity in terms of the Borel reducibili...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2015
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2014.60