On monomorphic topological functors with finite supports

Abstract

We prove that a monomorphic functor $F:Comp\to Comp$ with finite supports is epimorphic, continuous, and its maximal $\emptyset$-modification $F^\circ$ preserves intersections. This implies that a monomorphic functor $F:Comp\to Comp$ of finite degree $deg F\le n$ preserves (finite-dimensional) compact ANR's if the spaces $F\emptyset$, $F^\circ\emptyset$, and $Fn$ are finite-dimensional ANR's. This improves a known result of Basmanov.