Sign up or sign in
logo
  1. Topology and Dynamics
  2. Icon: chevron
  3. STDC
  4. Icon: chevron
  5. 2024

Set-Theoretic Topology

‟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 $Y$.