Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets

Daniel Azagra, Tadeusz Dobrowolski, Miguel García-Bravo

Let $E$, $F$ be separable Hilbert spaces, and assume that $E$ is infinite-dimensional. We show that for every continuous mapping $f:E\to F$ and every continuous function $\varepsil…