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Journal of Logic and Computation Advance Access originally published online on September 10, 2007
Journal of Logic and Computation 2007 17(6):1063-1081; doi:10.1093/logcom/exm034
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Partial Continuous Functions and Admissible Domain Representations

Fredrik Dahlgren

Department of Mathematics, Uppsala Universitet, PO Box 480, 751 06 Uppsala, Sweden. E-mail: fredrik.dahlgren{at}math.uu.se

Received 20 October 2006.


  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 the category of admissibly representable spaces with morphisms functions which are representable by a partial continuous function is Cartesian closed. Finally, we consider the question of effectivity.

Keywords: Domain theory; domain representations; computability theory; computable analysis


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