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On differentiability of Peano type functions. III


Authors: Jacek Cichoń and Michał Morayne
Journal: Proc. Amer. Math. Soc. 92 (1984), 432-438
MSC: Primary 26A03; Secondary 04A30
DOI: https://doi.org/10.1090/S0002-9939-1984-0759669-5
MathSciNet review: 759669
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Abstract: We show that for all positive natural numbers $ m$,$ n$ the following two sentences are equivalent: (i) $ {2^{{\aleph _0}}} \leqslant {\aleph _n}$; (ii) there exists an onto function $ f:{R^n} \to {R^{n + m}}$ ($ R$ the set of real numbers) such that at each point of $ {R^n}$ at least $ n$ coordinates of $ f$ are differentiable.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0759669-5
Keywords: Continuum hypothesis, differentiability, Peano function, Lipschitz condition
Article copyright: © Copyright 1984 American Mathematical Society