Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

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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 ... continued below

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Farmer, Matthew Ray August 2011.

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  • Farmer, Matthew Ray

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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.

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  • August 2011

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  • May 17, 2012, 9:47 p.m.

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  • June 26, 2012, 10:51 a.m.

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Farmer, Matthew Ray. Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces, dissertation, August 2011; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc84202/: accessed June 27, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .