Compositio Mathematica

Research Article

Transversality theorem in o-minimal structures

Ta Lê Loia1

a1 Department of Mathematics, University of Dalat, Dalat, Vietnam (email: taleloi@hotmail.com)

Abstract

In this paper we present Thom’s transversality theorem in o-minimal structures (a generalization of semialgebraic and subanalytic geometry). There are no restrictions on the differentiability class and the dimensions of manifolds involved in comparison withthe general case.

(Received August 10 2007)

(Accepted January 09 2008)

(Online publication July 22 2008)

2000 Mathematics subject classification

  • 32B20;
  • 58C27;
  • 14P10

Keywords

  • o-minimal structures;
  • transversality