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Berthiaume, Gilles (1976) Contributions to the theory of correspondences and hyperspaces. Doctoral thesis, Keele University.
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Abstract
The object of this thesis is to study topological properties of. correspondences, or set-valued mappings, and hyperspaces, i.e, spaces of subsets of given sets.
In chapter 1, we study correspondences under their purely set-theoretical aspect. We introduce canonical extensions and stress their usefulness in proving properties of correspondences.
Chapter 2 is devoted to topological structures on hyperspaces, including the finite topology and quasi-uniformities. Chapter 3 pursues that study. The unifying role of quasi-uniformities is discussed: not only do they often yield a common proof of different results, they also give way to new ones.
Finally, chapter 4 deals with so-called "covering topologies", such as the locally finite topology. We study their properties and.compare them with the uniform and the finite topologies.
Item Type: | Thesis (Doctoral) |
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Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Natural Sciences > School of Computing and Mathematics |
Depositing User: | Lisa Bailey |
Date Deposited: | 09 May 2019 08:14 |
Last Modified: | 09 May 2019 08:14 |
URI: | https://eprints.keele.ac.uk/id/eprint/6294 |