Functors that carry connected ANR-bicompacta to simply connected spaces
This paper studies continuous monomorphic functors F on the category of bicompacta. Let k be a k-point discrete space, X a bicompactum and C(k,X) the space of continuous mappings from k to X with the compact-open topology. There is a continuous mapping C(k,X)\(\times F(k)\to F(X)\) adjoint to the structural continuous map C(k,X)\(\to C(F(k),F(X))\). Let \(F_ k(X)\) be the image of this mapping and say F has degree n if \(F_ n(X)=F(X)\) for all bicompacta X. The principle result is the following: If F preserves intersections and the empty set, has finite degree n, and is such that F(n) is an ANR and F(I) is linearly connected then the functor F carries connected ANR- bicompacta to simply connected spaces if and only if \(F(S^ 1)\) is a simply connected space.
scientific article; zbMATH DE number 3925784