Decomposing Euclidean Space with a Small Number of Smooth Sets


Juris Steprans

26 pages, to appear in Trans. Amer. Math. Soc.

Let the cardinal invariant s_n denote the least number of continuously smooth n-dimensional surfaces into which (n+1)-dimensional Euclidean space can be decomposed. It will be shown to be consistent that s_n is greater than s_(n+1). These cardinals will be shown to be closely related to the invariants associated with the problem of decomposing continuous functions into differentiable ones.

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