# Ding Longyun: On generalisation of the Jayne-Rogers Theorem

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 31 August 2016, 17:00 hrs

Room: S17#04-05, Department of Mathematics, NUS

Speaker: Ding Longyun

Title: On generalisation of the Jayne-Rogers Theorem

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Let X,Y be separable metrizable spaces with X analytic, and let
f be function from X to Y. We say f is Sigma-m-n if, for any
Sigma-n subset A of Y, the preimage of A under f is Sigma-m.
A theorem of Jayne-Rogers shows that, a function f is Sigma-2-2 iff
X can be decomposed into countably many Sigma-2 subsets such that
f is continuous on each of these subsets. In this talk, we will
generalize this theorem to Sigma-m-n with n leq m =3 .
We also survey the history of the study on decomposing Borel functions.