A counterexample to infinite-dimensional version of the Morse-Sard theorem
The author establishes that the Morse criticality theorem can not be extended to infinite-dimensional Banach spaces. More precisely, an example is provided showing that there exists a smooth rank-1 real map \(j\) defined on \(l^2\) such that \(j(A)\) has nonempty interior, for some subset \(A\) of \(l^2\) of critical points with finite Hausdorff dimension.
scientific article; zbMATH DE number 1931540