García Bravo, Miguel2025-02-072025-02-07202010.1016/j.jmaa.2019.123535https://hdl.handle.net/20.500.14352/117924Let E be an infinite-dimensional separable Hilbert space. We show that for every C1 function f : E → Rd, every open set U with Cf := {x ∈ E : Df(x) is not surjective} ⊂ U and every continuous function ε : E → (0, ∞) there exists a C1 mapping ϕ : E → Rd such that ||f(x) −ϕ(x)|| ≤ ε(x)for every x ∈ E, f =ϕoutside U and ϕhas no critical points (Cϕ = ∅). This result can be generalized to the case where E = c0 or E = lp, 1 <p < ∞. In the case E = c0 it is also possible to get that ||Df(x) −Dϕ(x)|| ≤ ε(x)for every x ∈ E.engjournal articlehttps://doi.org/10.1016/j.jmaa.2019.123535restricted accessBanach spaceMorse-Sard theoremApproximationCritical pointDiffeomorphic extractionCiencias12 Matemáticas