2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78659An explanation to the boundness of minimal log discrepancies conjectured by V.V. Shokurov would be that the minimal log discrepancies of a variety in its closed points define a lower semi-continuous function. We check this lower semi-continuity behaviour for varieties of dimension at most 3 and for toric varieties of arbitrary dimension.17 pages, LATEXAlgebraic Geometry14B05;14E30text