Results 11 to 20 of about 5,027 (259)
Borel structures on the set of Borel mappings
Topology and its Applications, 2012 In the paper [Pac. J. Math. 1, 5--31 (1951; Zbl 0044.11801)], \textit{R. Arens} and \textit{J. Dugundji} introduced and studied several types of topologies on the spaces of continuous functions such as admissible, proper and splitting topologies. In the paper under review, the authors study analogously Borel splitting and admissible structures on the ...
Georgiou, Dimitris +2 more
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Borel canonization of analytic sets with Borel sections
Proceedings of the American Mathematical Society, 2018 Kanovei, Sabok and Zapletal asked whether every proper σ \sigma
Ohad Drucker
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International Journal of Game Theory, 2003 The authors consider an \(n\)-person stochastic game with a Borel state space and compact metric action sets. Under some measurability and continuity conditions, the following holds: If the payoff to each player \(i\) is 1 or 0 according to whether or not the stochastic process stays forever in a given Borel set \(G_i\) then there exists a Nash ...
Ashok P. Maitra, William D. Sudderth
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Borel Directions and Uniqueness of Meromorphic Functions [PDF]
Abstract and Applied Analysis, 2013 We investigate the relationship between Borel directions and uniqueness of meromorphic functions and obtain some results of meromorphic functions sharing four distinct values IM and one set in an angular domain containing a Borel line.
Keyu Zhang, HongYan Xu, Hongxun Yi
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PARTITIONING THE REAL LINE INTO BOREL SETS
The Journal of Symbolic Logic, 2023 AbstractFor which infinite cardinals $\kappa $ is there a partition of the real line ${\mathbb R}$ into precisely $\kappa $ Borel sets? Work of Lusin, Souslin, and Hausdorff shows that ${\mathbb R}$ can be partitioned into $\aleph _1$ Borel sets. But other than this, we show that the spectrum of possible sizes of partitions of ${\mathbb R}$
Brian, Will
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Frucht’s theorem in Borel setting
Periodica Mathematica Hungarica, 2023 In this paper, we show that Frucht's theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic ...
Onur Bilge, Burak Kaya
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Representing Probability Measures using Probabilistic Processes [PDF]
, 2006 In the Type-2 Theory of Effectivity, one considers representations of topological spaces in which infinite words are used as "names" for the elements they represent.
Schröder , Matthias +3 more
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Amenability, Countable Equivalence Relations, and Their Full Groups [PDF]
, 2008 This thesis consists of an introduction and four independent chapters. In Chapter 1, we study homeomorphism groups of metrizable compactifications of the natural numbers. Those groups can be represented as almost zero-dimensional Polishable subgroups
Tsankov, Todor Dimitrov
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Structure of the set of Borel exceptional vectors for entire curves
Математичні Студії, 2020 It is proved that the structure of the set of Borel exceptional vectors for transcendental entire curve something likes structure of the set of Nevanlinna deficient vectors for entire curve of finite order.
A.I. Bandura, Ya.I. Savchuk
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Proceedings of the American Mathematical Society, 1986 Topological characterizations of all zero-dimensional homogeneous absolute Borel sets are obtained; it turns out that there are ω 1 {\omega _1} such spaces. We use results from game theory—particularly, about Wadge classes.
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