Locally Non-compact Spaces and Continuity Rinciples

Alexander Simpson, Andrej Bauer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We give a constructive proof that Baire space embeds in any inhabited locally non-compact complete separable metric space, X, in such a way that every sequentially continuous function from Baire space to Z extends to a function from X to R. As an application, we show that in the presence of certain choice and continuity principles, the statement \all functions from X to R is continuous" is false. This generalizes a result previously obtained by Ecardo and Streicher, in the context of \domain realizability", for the special case X = C[0; 1].
Original languageEnglish
Title of host publicationProceedings of International Conference on Computability and Complexity in Analysis
PublisherFernuniversitat Hagen Informatik Berichte
Pages103-116
Number of pages14
Volume302
Edition8
Publication statusPublished - 2003

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