Submission date: 9 January 2007; revised versions 6 July 2007; 27 September 2007.

Abstract:

A main tool in studying topological properties of sets definable in o-minimal structures is the Cell Decomposition Theorem. This paper proposes its metric counterpart. It is shown that in decomposing into Lipschitz cells permutations of cartesian coordinates are sufficient.

Mathematics Subject Classification: Primary 32B20, 14P10. Secondary 32S60, 51N20, 51F99

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

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