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A countable CW complex K is quasi-finite (as defined by A. Karasev) if for every finite subcomplex M of K there is a finite subcomplex e(M) such that any map f: A → M, where A is closed in a separable metric space X satisfying XτK, has an extension g: X → e(M). Levin's results imply that none of the Eilenberg-MacLane spaces K(G,2) is quasi-finite if G ≠ 0. In this paper we discuss quasi-finiteness of all Eilenberg-MacLane spaces. More generally, we deal with CW complexes with finitely many...
The paper is devoted to generalizations of the Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to their homology groups. Here are the main results of the paper:
Theorem 0.1. Let L be a nilpotent CW complex and F the homotopy fiber of the inclusion i of L into its infinite symmetric product SP(L). If X is a metrizable space such that for all k ≥ 1, then and for all k ≥ Theorem 0.2. Let X be a metrizable space such that dim(X) < ∞ or X ∈ ANR. Suppose...
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