We prove that for every compactum with there is a cell-like resolution from a compactum onto such that and for every integer and every abelian group such that we have . The latter property implies that for every simply connected CW–complex such that we also have .
"Cell-like resolutions preserving cohomological dimensions." Algebr. Geom. Topol. 3 (2) 1277 - 1289, 2003. https://doi.org/10.2140/agt.2003.3.1277