Partial Continuous Functions and Admissible Domain Representations

  • Fredrik Dahlgren
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

It is well known that to be able to represent continuous functions between domain representable spaces it is critical that the domain representations of the spaces we consider are dense. In this article we show how to develop a representation theory over a category of domains with morphisms partial continuous functions. The raison d’être for introducing partial continuous functions is that by passing to partial maps, we are free to consider totalities which are not dense. We show that there is a natural subcategory of the category of representable spaces with morphisms representable maps which is Cartesian closed. Finally, we consider the question of effectivity.

Keywords

Domain theory domain representations computability theory computable analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fredrik Dahlgren
    • 1
  1. 1.Department of mathematicsUniversity of UppsalaUppsalaSweden

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