Computable analysis: an introduction
Computable analysis: an introduction
Admissible Representations of Limit Spaces
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Type Theory via Exact Categories
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The realizability approach to computable analysis and topology
The realizability approach to computable analysis and topology
Comparing Functional Paradigms for Exact Real-Number Computation
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Continuous Functionals of Dependent Types and Equilogical Spaces
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Quotients of countably based spaces are not closed under sobrification
Mathematical Structures in Computer Science
Compactly generated domain theory
Mathematical Structures in Computer Science
A Convenient Category of Domains
Electronic Notes in Theoretical Computer Science (ENTCS)
Two preservation results for countable products of sequential spaces
Mathematical Structures in Computer Science
On the Relationship between Filter Spaces and Weak Limit Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Reducibility of domain representations and cantor–weihrauch domain representations
Mathematical Structures in Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Computational Effects in Topological Domain Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
Comparing free algebras in Topological and Classical Domain Theory
Theoretical Computer Science
Admissible representations in computable analysis
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Computability on random events and variables in a computable probability space
Theoretical Computer Science
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There are two main approaches to obtaining ‘topological’ cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed – for example, the category of sequential spaces. Under the other, one generalises the notion of space – for example, to Scott's notion of equilogical space. In this paper, we show that the two approaches are equivalent for a large class of objects. We first observe that the category of countably based equilogical spaces has, in a precisely defined sense, a largest full subcategory that can be simultaneously viewed as a full subcategory of topological spaces. In fact, this category turns out to be equivalent to the category of all quotient spaces of countably based topological spaces. We show that the category is bicartesian closed with its structure inherited, on the one hand, from the category of sequential spaces, and, on the other, from the category of equilogical spaces. We also show that the category of countably based equilogical spaces has a larger full subcategory that can be simultaneously viewed as a full subcategory of limit spaces. This full subcategory is locally cartesian closed and the embeddings into limit spaces and countably based equilogical spaces preserve this structure. We observe that it seems essential to go beyond the realm of topological spaces to achieve this result.