Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Partial Continuous Functions and Admissible Domain Representations

Speaker: Fredrik Dahlgren
Presentation: swansea.pdf
Slot: Mon, 10:30-10:50, Faraday D (col. 4)

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'Ítre 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. 


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