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Reducibility of Domain Representations and CantorWeihrauch Domain Representations
, 2006
"... 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 preorder on representatio ..."
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Cited by 8 (4 self)
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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 preorder 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, nontriviality. 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. 1.
EFFECTIVE STRUCTURE THEOREMS FOR SPACES OF COMPACTLY SUPPORTED DISTRIBUTIONS
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Cantor–Weihrauch domain representations
, 2007
"... We hope you have now downloaded a proof of your paper in pdf format, and also the Transfer of ..."
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We hope you have now downloaded a proof of your paper in pdf format, and also the Transfer of
12345efghi UNIVERSITY OF WALES SWANSEA REPORT SERIES
"... Computability on topological spaces via domain representations by V StoltenbergHansen and J V Tucker Report # CSR 22007Computability on topological spaces via domain representations ..."
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Computability on topological spaces via domain representations by V StoltenbergHansen and J V Tucker Report # CSR 22007Computability on topological spaces via domain representations