On differentiability of Peano type functions. III
Jacek Cichoń, Michał Morayne · Proceedings of the American Mathematical Society · 1984
We show that for all positive natural numbers m m , n n the following two sentences are equivalent: (i) 2 ℵ 0 ⩽ ℵ n {2^{{\aleph _0}}} \leqslant {\aleph _n} ; (ii) there exists an onto function f : R n → R n + m f:{R^n} \to {R^{n + m}} ( R R the set of real numbers) such that at each point of R n {R^n} at least n n coordinates of f f are differentiable.