Locally Non-compact Spaces and Continuity Rinciples

Alexander Simpson; Andrej Bauer

Locally Non-compact Spaces and Continuity Rinciples

Alexander Simpson, Andrej Bauer

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Proceedings of International Conference on Computability and Complexity in Analysis
Publisher	Fernuniversitat Hagen Informatik Berichte
Pages	103-116
Number of pages	14
Volume	302
Edition	8
Publication status	Published - 2003

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title = "Locally Non-compact Spaces and Continuity Rinciples",

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].",

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year = "2003",

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volume = "302",

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AU - Simpson, Alexander

AU - Bauer, Andrej

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N2 - 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].

AB - 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].

M3 - Conference contribution

VL - 302

SP - 103

EP - 116

BT - Proceedings of International Conference on Computability and Complexity in Analysis

PB - Fernuniversitat Hagen Informatik Berichte

ER -

Locally Non-compact Spaces and Continuity Rinciples

Abstract

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