%0 Journal Article
%T Level Sets of Differentiable Functions of Two Variables with Non-vanishing Gradient
%A M¨¢rton Elekes
%J Mathematics
%D 2011
%I arXiv
%X We show that if the gradient of $f:\RR^2\rightarrow\RR$ exists everywhere and is nowhere zero, then in a neighbourhood of each of its points the level set $\{x\in\RR^2:f(x)=c\}$ is homeomorphic either to an open interval or to the union of finitely many open segments passing through a point. The second case holds only at the points of a discrete set. We also investigate the global structure of the level sets.
%U http://arxiv.org/abs/1109.4959v1