2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62746We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields.20 pagesAlgebraic Topology55U35text