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 |
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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 |