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].
|Title of host publication||Proceedings of International Conference on Computability and Complexity in Analysis|
|Publisher||Fernuniversitat Hagen Informatik Berichte|
|Number of pages||14|
|Publication status||Published - 2003|