A topological version of a combinatorial theorem of Katětov
Aleksander Błaszczyk, Dok Yong Kim · Czech digital mathematics library · 1988
We prove that for every fixed-point-free homeomorphism f of a O-dimensional paracompact space X onto a closed subset of X there exists a partition -{U, ,U 2 ,U-j} of X consisting of closed-open sets such that f(u\)nU.==0 for every i £, 3.