Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A03, 04A30

Retrieve articles in all journals with MSC: 26A03, 04A30


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

American Mathematical Society