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Vietnam Journal of Mathematics 38:3 (2010) 281-286  

 

An Observation on Definable Bi-Lipschitz Homeomorphism

Ta Le Loi

 

Abstract. This short note gives an observation on the directional derivatives of bi-Lipschitz homeo-morphisms that are definable in o-minimal structures and, as a conse-quence, it implies that the dimension of directional sets of definable sets is invariant under definable bi-Lipschitz homeomorphisms.

2000 Mathematics Subject Classification: 14P15, 32B20, 14P10, 57R45.

Keywords: o-minimal structure, bi-Lipschitz homeomorphism, direction set.

 

 

 

 

 

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