The Relative Complexity of Various Classification Problems among Compact Metric Spaces

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In this thesis, we discuss three main projects which are related to Polish groups and their actions on standard Borel spaces. In the first part, we show that the complexity of the classification problem of continua is Borel bireducible to a universal orbit equivalence relation induce by a Polish group on a standard Borel space. In the second part, we compare the relative complexity of various types of classification problems concerning subspaces of [0,1]^n for all natural number n. In the last chapter, we give a topological characterization theorem for the class of locally compact two-sided invariant non-Archimedean Polish groups. … continued below

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vi, 61 pages : illustrations

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Chang, Cheng May 2016.

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  • Chang, Cheng

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In this thesis, we discuss three main projects which are related to Polish groups and their actions on standard Borel spaces. In the first part, we show that the complexity of the classification problem of continua is Borel bireducible to a universal orbit equivalence relation induce by a Polish group on a standard Borel space. In the second part, we compare the relative complexity of various types of classification problems concerning subspaces of [0,1]^n for all natural number n. In the last chapter, we give a topological characterization theorem for the class of locally compact two-sided invariant non-Archimedean Polish groups. Using this theorem, we show the non-existence of a universal group and the existence of a surjectively universal group in the class.

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vi, 61 pages : illustrations

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  • May 2016

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  • June 28, 2016, 4:28 p.m.

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  • March 5, 2021, 12:35 p.m.

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Thumbnail image of item number 1 in: 'The Relative Complexity of Various Classification Problems among Compact Metric Spaces'.
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Chang, Cheng. The Relative Complexity of Various Classification Problems among Compact Metric Spaces, dissertation, May 2016; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc849626/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

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