Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

• Main Author: Farmer, Matthew Ray
• Other Authors: Kallman, Robert R.
• Format: Others
• Language: English
• Published: University of North Texas 2011
• Subjects: Strong Choquet; Baire category; analysis; topology; game theory; Banach spaces
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc84202/

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.