Subject: Stasheff's second question From: Martin.A.Arkowitz@Dartmouth.EDU (Martin A. Arkowitz) Date: 25 Oct 2005 18:18:08 EDT With regard to Jim's question for a reference for "For any topological space X (for example infinite dimensional), we have H_*(X)_singular=lim_{K-->X} H_*(K)_singular, where the limit is taken over all finite CW-complexes mapping to X", the book of Cooke and Finney, "Homology of Cell Complexes", is relevant. On pp. 183 - 186 the singular homology groups are defined this way (using finite, regular complexes). It is then proved (p. 204) that this is isomorphic to the homology of a regular (not necessarily finite) complex.