Real Algebraic and Analytic Geometry Preprint Server

e-mail:

Submission: 2007, September 27.

Abstract:
A main tool in studying topological properties of sets definable in o- minimal structures is the Cell Decomposition Theorem. The present paper proposes its metric counterpart based on the idea of a Lipschitz cell. In contrast to earlier results, we give an algorithm of a Lipschitz cell decomposition involving only permu- tations of variables as changes of coordinates.

Mathematics Subject Classification (2000): 32B20, 14P10. 32S60, 51N20, 51F99.

Keywords and Phrases: M-cell, semi-M-cell, M-disc, Lipschitz mapping, cell decomposition.

Full text, 20p.: pdf 208k.