Necessary and sufficient condition of Morse-Sard theorem for real valued functions
Necessary and sufficient condition is given for a set $A\subset R^1$ to be a subset of the critical values set for a $C^k$ function $f:R^m \to R^1$.
math.CA↗
arXiv subjects
Azat Ainouline
Publications and source records attributed to Azat Ainouline.
Vector valued functions not constant on connected sets of critical points
Whitney type examples of maps $f\in C^k(\real^m,\real^n)$ for a maximal possible real $k$, and multidimensional space-filling curves with special properties are constructed.
math.GT↗
Real Valued Dimension For Morse-Sard Theorem
A dimension allowing in particular to state necessary and sufficient conditions of the Morse-Sard Theorem for real valued functions is introduced.
math.GT↗