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Title: Contributions to the theory of correspondences and hyperspaces
Author: Berthiaume, Gilles
Awarding Body: Keele University
Current Institution: Keele University
Date of Award: 1976
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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 them with the uniform and the finite topologies.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics