Abstract
General methods of investigating effectivity on regular Hausdor dorff (T 3) spaces is considered. It is shown that there exists a functor from a category of T 3 spaces into a category of domain representations. Using this functor one may look at the subcategory of effective domain representations to get an effectivity theory for T 3 spaces. However, this approach seems to be beset by some problems. Instead, a new approach to introducing effectivity to T 3 spaces is given. The construction uses effective retractions on effective Scott-Ershov domains. The benefit of the approach is that the numbering of the basis and the numbering of the elements are derived at once.
Supported by STINT, The Swedish Foundation for International Cooperation in Research and Higher Education.
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Blanck, J. (2001). Effectivity of Regular Spaces. In: Blanck, J., Brattka, V., Hertling, P. (eds) Computability and Complexity in Analysis. CCA 2000. Lecture Notes in Computer Science, vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45335-0_1
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DOI: https://doi.org/10.1007/3-540-45335-0_1
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