We have
\[ \chi _{\mathcal{P}\webleft (X\webright )}\webleft (\chi _{x},\chi _{U}\webright )=\chi _{U}\webleft (x\webright ) \]
for each $x\in X$, giving an equality of functions
\[ \chi _{\mathcal{P}\webleft (X\webright )}\webleft (\chi _{\webleft (-\webright )},\chi _{U}\webright )=\chi _{U}. \]
