Locally Non-compact Spaces and Continuity Principles
نویسندگان
چکیده
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 Escardó and Streicher, in the context of “domain realizability”, for the special case X = C[0, 1].
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