2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142716For $θ$ a non-algebraic point on a quasi projective variety over a number field, I prove that $θ$ has an approximation by a series of algebraic points of bounded height and degree which is essentially best possible. Applications of this result will include a proof of a slightly strengthened version of the Philippon criterion, some new algebraic independence criteria, statements concerning metric transcendence theory on varieties of arbitrary dimension, and a rather accurate estimate for the number of algebraic points of bounded height and degree on quasi projective varieties over number fields.42 pagesNumber TheoryAlgebraic Geometry11J13; 11J81; 11J85; 14G40; 14G17; 11J83; 14J20; 11G50; 14G25; 11G35text