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Set-Theoretic Topology
‟Adding a continuous map by forcing” by Akira Iwasa <akiraiwasa94@gmail.com>, Howard College
‟Adding a continuous map by forcing” by Akira Iwasa <akiraiwasa94@gmail.com>, Howard College
‟Adding a continuous map by forcing” by Akira Iwasa <akiraiwasa94@gmail.com>, Howard College
‟Adding a continuous map by forcing” by Akira Iwasa <akiraiwasa94@gmail.com>, Howard College
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 $Y$.