2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228082We use functoriality of tropicalization and the geometry of projections of subvarieties of tori to show that the fibers of the tropicalization map are dense in the Zariski topology. For subvarieties of tori over fields of generalized power series, points in each tropical fiber are obtained "constructively" using Kedlaya's transfinite version of Newton's method.11 pages. v2: added footnote explaining gap in earlier proofs of surjectivity of tropicalization, other minor changes. To appear in Math. ZAlgebraic Geometry12J25, 16W60, 14G22text