Real Algebraic and Analytic Geometry
Submission: 2004, April 22.
For constructions with differentiable functions in o-minimal structures one needs partitions of definable sets. The strata or cells of such partitions shall have some suitable properties, i.e. the cells shall be defined by graphs of m times differentiable functions, and the derivatives of these functions shall have certain bounding properties. Here we generalize the decomposition, used by Kurdyka and Pawlucki to prove a subanalytic version of Whitney's extension theorem, to arbitrary o-minmal structures expanding a real closed field.
Mathematics Subject Classification (2000): 03C64 57N80.
Keywords and Phrases: cell decomposition, o-minimal structures, stratification.
Full text, 14p.: dvi 67k, ps.gz 160k, pdf 229k.