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Adding a continuous map by forcing

Akira Iwasa ⟨akiraiwasa94@gmail.com⟩

Abstract:

We discuss in what circumstances forcing adds new continuous maps. We prove that if X is scattered compact Hausdorff and Y is discrete, then forcing does not add any continuous maps from X to Y. On the other hand, if X is not a zero-dimensional scattered pseudocompact space and Y has more than one point, then ccc forcing adds a continuous map from X to Y.

Status: Accepted

Collection: Set-Theoretic Topology

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