2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62956We show that a continuous local semiflow of $C^k$-maps on a finite-dimensional $C^k$-manifold M can be embedded into a local $C^k$-flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [fil/tei:01]. We prove that finite-dimensional realizations for interest rate models are highly regular objects, namely given by submanifolds M of $D(A^{\infty})$, where A is the generator of a strongly continuous semigroup.Functional AnalysisDifferential Geometry60H15, 46A04, 53C12text