Submission date: 7 April 2011

Abstract:

Let X be a definably compact definable C^r manifold and 2 \le r <\infty. We prove that the set of definable Morse functions is open and dense in the set of definable C^r functions on X with respect to the definable C2 topology.

Mathematics Subject Classification: 14P10, 14P20, 57R35, 58A05, 03C64.

Keywords and phrases: O-minimal, real closed fields, Morse theory, definable C^r functions, critical points, critical values, definably compact.

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