# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Wadge Hierarchy on 0-dimensional Polish space"

#### Scamperti, Salvatore

Joint work with Raphaël Carroy (University of Turin) and Luca Motto Ros (University of Turin). Given two topological spaces $X$ and $Y$, a continuous reduction from $A \subseteq X$ to $B \subseteq Y$ is a continous function $f: X \to Y$ satisfying $f^{-1}(B) = A$. In this case we say that $A$ Wadge reduces to $B$. Wadge theory has received a lot of attention, but the complete description of the Wadge hierarchy, up to order-isomorphism, for all zero-dimensional spaces under AD had never been done. The purpose of the talk is to give such description.

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