Computability
Algebraic and fixed point equations over inverse limits of algebras
Theoretical Computer Science
Mathematical theory of domains
Mathematical theory of domains
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Selected papers of the workshop on Topology and completion in semantics
Handbook of logic in computer science (vol. 4)
Handbook of logic in computer science (vol. 3)
Real number computability and domain theory
Information and Computation
A hierarchy of domains with totality, but without density
Computability, enumerability, unsolvability
A computational model for metric spaces
Theoretical Computer Science
Foundation of a computable solid modeling
Proceedings of the fifth ACM symposium on Solid modeling and applications
Effective domain representations of H (X), the space of compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Concrete models of computation for topological algebras
Theoretical Computer Science - Special issue on computability and complexity in analysis
Domain representations of topological spaces
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Computable functions and semicomputable sets on many-sorted algebras
Handbook of logic in computer science
Theoretical Computer Science
Domain Theory and Differential Calculus (Functions of one Variable)
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Infinite Systems of Equations over Inverse Limits and Infinite Synchronous Concurrent Algorithms
Proceedings of the REX Workshop on Sematics: Foundations and Applications
Type Theory via Exact Categories
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Topological and limit-space subcategories of countably-based equilogical spaces
Mathematical Structures in Computer Science
Theoretical Computer Science - Mathematical foundations of programming semantics
Abstract versus concrete computation on metric partial algebras
ACM Transactions on Computational Logic (TOCL)
Partial Continuous Functions and Admissible Domain Representations
Journal of Logic and Computation
Domain representations of spaces of compact subsets
Mathematical Structures in Computer Science
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We introduce a notion of reducibility of representations of topological spaces and study some basic properties of this notion for domain representations. A representation reduces to another if its representing map factors through the other representation. Reductions form a pre-order on representations. A spectrum is a class of representations divided by the equivalence relation induced by reductions. We establish some basic properties of spectra, such as, non-triviality. Equivalent representations represent the same set of functions on the represented space. Within a class of representations, a representation is universal if all representations in the class reduce to it. We show that notions of admissibility, considered both for domains and within Weihrauch's TTE, are universality concepts in the appropriate spectra. Viewing TTE representations as domain representations, the reduction notion here is a natural generalisation of the one from TTE. To illustrate the framework, we consider some domain representations of real numbers and show that the usual interval domain representation, which is universal among dense representations, does not reduce to various Cantor domain representations. On the other hand, however, we show that a substructure of the interval domain more suitable for efficient computation of operations is equivalent to the usual interval domain with respect to reducibility.