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Computability on Topological Spaces via Domain Representations

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New Computational Paradigms

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Uppsala University, S-75106, Uppsala, Sweden

    Viggo Stoltenberg-Hansen

  2. Department of Computer Science, University of Wales Swansea, SA2 8PP, Wales, UK

    John V. Tucker

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  1. Viggo Stoltenberg-Hansen
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  2. John V. Tucker
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Editors and Affiliations

  1. University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, Netherlands

    Benedikt Löwe

  3. Università di Siena, Pian dei Mantellini 44, 53100, Siena, Italy

    Andrea Sorbi

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Stoltenberg-Hansen, V., Tucker, J.V. (2008). Computability on Topological Spaces via Domain Representations. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) New Computational Paradigms. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68546-5_8

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