2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121711Paradigms of bilinear maps f between locally convex spaces (like evaluation or composition) are not continuous, but merely hypocontinuous. We describe situations where, nonetheless, compositions of f with Keller C^n_c-maps (on suitable domains) are C^n_c. Our main applications concern holomorphic families of operators, and the foundations of locally convex Poisson vector spaces.21 pages, LaTeX (v2: discussion of non-reflexive Poisson vector spaces and further material added; extended preprint version)Functional AnalysisMathematical Physics26E15; 26E20 (primary) 17B63; 22E65; 46A32; 46G20; 46T25 (secondary)text