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University of North Texas

1. Shi, Xiaohui. Graev Metrics and Isometry Groups of Polish Ultrametric Spaces.

Degree: 2013, University of North Texas

This dissertation presents results about computations of Graev metrics on free groups and characterizes isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. In Chapter 2, computations of Graev metrics are performed on free groups. One of the related results answers an open question of Van Den Dries and Gao. In Chapter 3, isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces are characterized. The notion of generalized tree is defined and a correspondence between the isomorphism group of a generalized tree and the isometry group of a Heine-Borel Polish ultrametric space is established. The concept of a weak inverse limit is introduced to capture the characterization of isomorphism groups of generalized trees. In Chapter 4, partial results of isometry groups of uncountable compact ultrametric spaces are given. It turns out that every compact ultrametric space has a unique countable orbital decomposition. An orbital space consists of disjoint orbits. An orbit subspace of an orbital space is actually a compact homogeneous ultrametric subspace. Advisors/Committee Members: Gao, Su, Jackson, Steve, 1957-, Brozovic, Douglas.

Subjects/Keywords: Rotationally reduced; generalized tree; weak inverse limit

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Shi, X. (2013). Graev Metrics and Isometry Groups of Polish Ultrametric Spaces. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc271898/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Shi, Xiaohui. “Graev Metrics and Isometry Groups of Polish Ultrametric Spaces.” 2013. Thesis, University of North Texas. Accessed August 05, 2020. https://digital.library.unt.edu/ark:/67531/metadc271898/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Shi, Xiaohui. “Graev Metrics and Isometry Groups of Polish Ultrametric Spaces.” 2013. Web. 05 Aug 2020.

Vancouver:

Shi X. Graev Metrics and Isometry Groups of Polish Ultrametric Spaces. [Internet] [Thesis]. University of North Texas; 2013. [cited 2020 Aug 05]. Available from: https://digital.library.unt.edu/ark:/67531/metadc271898/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Shi X. Graev Metrics and Isometry Groups of Polish Ultrametric Spaces. [Thesis]. University of North Texas; 2013. Available from: https://digital.library.unt.edu/ark:/67531/metadc271898/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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