DMS Set Theoretic Topology Seminar

Speaker: Ziqin Feng

Abstract.  Let $X$ and $Y$ be spaces.   $X$ is said to be $Y$-selective if every lower semicontinuous mapping from $Y$ to the nonempty closed subsets of $X$ has a continuous selection.  Let $L$ be a convergent sequence with limit point; e.g., $L={1/n: n=1,2,…} \cup {0}$.  Assuming Martin’s Axiom, we construct a space $X$ which is $L$-selective but not $Q$-selective, where $Q$ is the space of rational numbers.  It is not known if there is such an example in ZFC.