Partial continuous functions and admissible domain representations

Authors:
Fredrik Dahlgren
Affiliations:
Department of mathematics, University of Uppsala, Uppsala, Sweden
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

Citing 8
Cited 0

Categories of partial maps

Information and Computation
Mathematical theory of domains

Mathematical theory of domains
Effective algebras

Handbook of logic in computer science (vol. 4)
Domain theory

Handbook of logic in computer science (vol. 3)
Domain representations of topological spaces

Theoretical Computer Science
Domain representations of partial functions, with applications to spatial objects and constructive volume geometry

Theoretical Computer Science
Extended admissibility

Theoretical Computer Science
Streams, Stream Transformers and Domain Representations

Proceedings of the ESPRIT Working Group 8533 on Prospects for Hardware Foundations: NADA - New Hardware Design Methods, Survey Chapters

Quantified Score

Hi-index	0.00

Visualization

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.