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- W4295118595 abstract "A subset of Euclidean space will be said to be $n$-smooth if it has an $n$-dimensional tangent plane at each of its points. Let ${frak d}_n$ denote the least number $n$-smooth sets into which $n+1$-dimensional Euclidean space can be decomposed. For each $n$ it is shown to be consistent that ${frak d}_n > {frak d}_{n+1} $. Moreover, the inequalities ${frak d}_{n+1}^+ geq ${frak d}_n$ are established where ${frak d}_1$ is defined to be the continuum. The cardinal invariant ${frak d}_2$ is shown to be the same as the least $kappa$ such that each continuous function from the reals to the reals can be decomposed into $kappa$ differentiable functions." @default.
- W4295118595 created "2022-09-10" @default.
- W4295118595 creator A5016634588 @default.
- W4295118595 date "1995-01-06" @default.
- W4295118595 modified "2023-10-18" @default.
- W4295118595 title "Decomposing with smooth sets" @default.
- W4295118595 doi "https://doi.org/10.48550/arxiv.math/9501204" @default.
- W4295118595 hasPublicationYear "1995" @default.
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