I have just learned from Sikorski Book diferentiation of several variables this fact:
there are no diffeomorphisms of $G\subseteq E^k$ to $G'\subseteq E^l$ for $l<k$ but they do exist for $l\geq k$. It seems strange for me, as all conditions are completely symetrical between $E^k$ and $E^l$ for the definition of diffeomorphisms: $f$ and $f^{-1} $ should exist and both should be of class $C^1$. Why this symmetry has been broken by possibility with $l\geq k$ and not for $l<k$ ? So why one direction is possible and the other is not possible?
EDIT: the source page
