On monomorphic topological functors with finite supports

Abstract

We prove that a monomorphic functor $F:CompoComp$ with finite supports isepimorphic, continuous,and its maximal $emptyset$-modification $F^circ$ preserves intersections. Thisimplies that a monomorphic functor $F:CompoComp$ of finite degree $deg Flen$ preserves (finite-dimensional) compact ANRs if the spaces $Femptyset$,$F^circemptyset$ and $Fn$ are finite-dimensional ANRs. This improves a knownresult of Basmanov.