Topological completeness properties seek to generalize the definition of complete metric space to the context of topologies. Chapter 1 gives an overview of some of these properties. Chapter 2 introduces domain theory, a field originally intended for use in theoretical computer science. Finally, Chapter 3 examines how this computer-scientific notion can be employed in the study of topological completeness in the form of domain representability. The connections between domain representability and other topological completeness properties are subsequently examined.
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Geometry and Topology | Mathematics | Physical Sciences and Mathematics
DeVilbiss, Matthew D., "Domain Representability and Topological Completeness" (2016). Honors Theses. 84.