On monomorphic topological functors with finite supports

Details On monomorphic topological functors with finite supports On monomorphic topological functors with finite supports

2010-04-03

arxiv.org/abs/1004.0457v2

Mathematics

Category Theory

6 pages

Scientific paper

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.

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