Sign up or sign in

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

Back to collection