Decomposing Euclidean space with a small number of smooth sets
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- by Juris Steprāns
- Trans. Amer. Math. Soc. 351 (1999), 1461-1480
- DOI: https://doi.org/10.1090/S0002-9947-99-02197-2
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Abstract:
Let the cardinal invariant ${\mathfrak s}_{n}$ 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 ${\mathfrak s}_{n}$ is greater than ${\mathfrak s}_{n+1}$. These cardinals will be shown to be closely related to the invariants associated with the problem of decomposing continuous functions into differentiable ones.References
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Bibliographic Information
- Juris Steprāns
- Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3
- Email: steprans@mathstat.yorku.ca
- Received by editor(s): March 9, 1995
- Received by editor(s) in revised form: May 5, 1997
- Additional Notes: Research for this paper was partially supported by NSERC of Canada. The author would also like to acknowledge that this paper has significantly benefitted from several remarks of A. Miller
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 1461-1480
- MSC (1991): Primary 04A30; Secondary 28A15
- DOI: https://doi.org/10.1090/S0002-9947-99-02197-2
- MathSciNet review: 1473455