Decomposing Euclidean space

with a small number of smooth sets

Author:
Juris Steprans

Journal:
Trans. Amer. Math. Soc. **351** (1999), 1461-1480

MSC (1991):
Primary 04A30; Secondary 28A15

MathSciNet review:
1473455

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Abstract | References | Similar Articles | Additional Information

Abstract: Let the cardinal invariant denote the least number of continuously smooth -dimensional surfaces into which -dimensional Euclidean space can be decomposed. It will be shown to be consistent that is greater than . 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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Additional Information

**Juris Steprans**

Affiliation:
Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3

Email:
steprans@mathstat.yorku.ca

DOI:
http://dx.doi.org/10.1090/S0002-9947-99-02197-2

Keywords:
Cardinal invariant,
Sacks real,
tangent plane,
covering number

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

Article copyright:
© Copyright 1999
American Mathematical Society