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University of North Texas

1. Farmer, Matthew Ray. Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces.

Degree: 2011, University of North Texas

In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapping. It is further shown that this collection under any topology in the aforementioned class of similar topologies is a strong Choquet space. Finally, a collection of category results are developed since strong Choquet spaces are also Baire spaces. Advisors/Committee Members: Kallman, Robert R., Iaia, Joseph, Gao, Su.

Subjects/Keywords: Strong Choquet; Baire category; analysis; topology; game theory; Banach spaces

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

APA (6th Edition):

Farmer, M. R. (2011). Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc84202/

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):

Farmer, Matthew Ray. “Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces.” 2011. Thesis, University of North Texas. Accessed September 19, 2020. https://digital.library.unt.edu/ark:/67531/metadc84202/.

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

MLA Handbook (7th Edition):

Farmer, Matthew Ray. “Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces.” 2011. Web. 19 Sep 2020.

Vancouver:

Farmer MR. Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces. [Internet] [Thesis]. University of North Texas; 2011. [cited 2020 Sep 19]. Available from: https://digital.library.unt.edu/ark:/67531/metadc84202/.

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

Council of Science Editors:

Farmer MR. Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces. [Thesis]. University of North Texas; 2011. Available from: https://digital.library.unt.edu/ark:/67531/metadc84202/

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

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