Adding a continuous map by forcing - Iwasa, Akira (Topology Proceedings, 2024)
We study how forcing adds continuous maps. We prove the following theorems. Let X be a completely regular space. (1) If X is a scattered compact Hausdorff space and Y is a discrete space, then forcing does not add any continuous maps from X to Y. (2) If X is not a zero-dimensional scattered pseudocompact space and Y is a topological space which has more than one point, then some ccc forcing adds a continuous map from X to Y. (3) If X is infinite and there is a homeomorphism from X onto X which is not the identity map, then some ccc forcing adds a homeomorphism from X onto X.