DMS Set Theoretic Topology Seminar

PLEASE NOTE NEW ROOM 246

Speaker: Gary Gruenhage

Abstract.  A space X is said to be Y-selective if every lower semi-continuous mapping F from the space Y to the non-empty closed subsets of X has a continuous selection, i.e., there is a continuous f from Y to X with f(y) in F(y) for each y in Y.   X is self-selective if it is X-selective.  R. Shen and H.J.K. Junnila asked if the space of ordinals less than or equal to the first uncountable ordinal is self-selective.  We show that it is not.