2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70467It is an open problem whether every continuous homomorphism between infinite-dimensional Lie groups is smooth. In this article, we show that every Hoelder continuous homomorphism is smooth.22 pages; v2: minor improvements; proof of Lemma 3.4 corrected to avoid problem with alpha=1/2Group TheoryFunctional Analysis22E65 (Primary) 26E15, 26E20, 26E30, 46T20, 58C20 (Secondary)text