## Partial Continuous Functions and Admissible Domain Representations (2007)

Venue: | the Journal of Logic and Computation |

Citations: | 7 - 2 self |

### BibTeX

@INPROCEEDINGS{Dahlgren07partialcontinuous,

author = {Fredrik Dahlgren},

title = {Partial Continuous Functions and Admissible Domain Representations},

booktitle = {the Journal of Logic and Computation},

year = {2007},

pages = {104}

}

### OpenURL

### 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. Key words. Domain theory, domain representations, computability theory, computable analysis. 1

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Citation Context ...e to view (D D , f) as a partial function from D to E. Categories of domains with morphisms partial continuous functions have been studied before by (among others) Plotkin and Fiore (c.f. [Plo85] and =-=[Fio94]-=-). Here a partial continuous function from D to E is a pair (U, f) where U ⊆ D is a Scott-open subset of D and f : U → E is a continuous function from U to E. However, this notion of a partial continu... |

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Citation Context ...Stoltenberg-Hansen, as well as the anonymous referee, for their many suggestions for improvements of this article. 1sbeen studied by (among others) Stoltenberg-Hansen, Blanck and Hamrin (c.f. [SH01], =-=[Bla00]-=- and [Ham05]). It turns out that it is often important that the representation (D, D R , δ) is dense. That is, that the set D R of δ-names is dense in D with respect to the Scott-topology on D. Howeve... |

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6 | Admissible Domain Representations of Topological Spaces
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(Show Context)
Citation Context ...Hansen, as well as the anonymous referee, for their many suggestions for improvements of this article. 1sbeen studied by (among others) Stoltenberg-Hansen, Blanck and Hamrin (c.f. [SH01], [Bla00] and =-=[Ham05]-=-). It turns out that it is often important that the representation (D, D R , δ) is dense. That is, that the set D R of δ-names is dense in D with respect to the Scott-topology on D. However, if (D, D ... |