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 $\varnothing$-modification $F^{\circ }$ preserves intersections. This implies that a monomorphic functor $F:Comp\to Comp$ of finite degree $degF\le n$ preserves (finite-dimensional) compact ANR's if the spaces $F\varnothing$, $F^{\circ }\varnothing$, and $Fn$ are finite-dimensional ANR's. This improves a known result of Basmanov.

6 pages