In Domain Realizability, not all Functionals on C[–1, 1] are Continuous
Copyright policy )In Domain Realizability, not all Functionals on C[–1, 1] are Continuous
Summary: In this note we exhibit a continuity principle for real-valued functions on \(C[-1,1]\) that is not validated by realizability over domains although it is validated by Kleene's functional realizability corresponding to Weihrauch's theory of type 2 effectivity.
- TU Darmstadt Germany
- University of Birmingham United Kingdom
Categorical semantics of formal languages, continuity principle, functional realizability, Continuous lattices and posets, applications, Higher-type and set recursion theory, realizability over domains, real-valued functions, type 2 effectivity, Constructive and recursive analysis
Categorical semantics of formal languages, continuity principle, functional realizability, Continuous lattices and posets, applications, Higher-type and set recursion theory, realizability over domains, real-valued functions, type 2 effectivity, Constructive and recursive analysis
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