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.

LaTeX 2e source file.

DVI and Postscript files are available at the Topology Atlas preprints side.