Remarks on the inverse and implicit function theorems for differentiable functions

Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces

“…Furthermore, the second-listed author [15] showed that C 1 vector fields with isolated critical points are local homeomorphisms given that the dimension of the ambient space is higher than 2. For the interest of readers, we refer to [2,3,4,6,7,8,9,11,12,13,18,20,21,23] for some relevant works in Euclidean spaces.…”