On differentiability of Peano type functions. III
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- by Jacek Cichoń and Michał Morayne PDF
- Proc. Amer. Math. Soc. 92 (1984), 432-438 Request permission
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
- H. G. Eggleston, Two measure properties of Cartesian product sets, Quart. J. Math. Oxford Ser. (2) 5 (1954), 108–115. MR 64850, DOI 10.1093/qmath/5.1.108
- Kazimierz Kuratowski and Andrzej Mostowski, Set theory, Second, completely revised edition, Studies in Logic and the Foundations of Mathematics, Vol. 86, North-Holland Publishing Co., Amsterdam-New York-Oxford; PWN—Polish Scientific Publishers, Warsaw, 1976. With an introduction to descriptive set theory; Translated from the 1966 Polish original. MR 0485384
- M. Morayne, On differentiability of Peano type functions, Colloq. Math. 48 (1984), no. 2, 261–264. MR 758535, DOI 10.4064/cm-48-2-261-264
- M. Morayne, On differentiability of Peano type functions, Colloq. Math. 48 (1984), no. 2, 261–264. MR 758535, DOI 10.4064/cm-48-2-261-264 S. Saks, Theory of the integral, Monografie Mat., vol. 7, PWN, Warsaw, 1937.
- Wacław Sierpiński, Sur quelques propositions concernant la puissance du continu, Fund. Math. 38 (1951), 1–13 (French). MR 48517, DOI 10.4064/fm-38-1-1-13
- Roman Sikorski, A characterization of alephs, Fund. Math. 38 (1951), 18–22. MR 48519, DOI 10.4064/fm-38-1-18-22 R. Solovay, Independence results in the theory of cardinals, Notices Amer. Math. Soc. 10 (1963), 595. Abstract #63T-395.
Additional Information
- © Copyright 1984 American Mathematical Society
- 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