In Domain Realizability, not all Functionals on C[–1, 1] are Continuous

Mathematical Logic Quarterly 48 (S1):41-44 (2002)
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Abstract

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

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