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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Computability on Topological Spaces via Domain Representations
verfasst von : Viggo Stoltenberg-Hansen, John V. Tucker
Erschienen in: New Computational Paradigms
Verlag: Springer New York
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Domains are ordered structures designed to model computation with approximations. We give an introduction to the theory of computability for topological spaces based on representing topological spaces and algebras using domains. Among the topics covered are different approaches to computability on topological spaces; orderings, approximations, and domains; making domain representations; effective domains; classifying representations; type two effectivity and domains; and special representations for inverse limits, regular spaces, and metric spaces. Lastly, we sketch a variety of applications of the theory in algebra, calculus, graphics, and hardware.