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.