Morse theory in definably complete d-minimal structures

2024/08/26 by Fujita, Masato, Kawakami, Tomohiro
#03C64 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2408.14675

Abstract

Consider a definable complete d-minimal expansion (F, <, +, ⋅, 0, 1, …,) of an oredered field F. Let X be a definably compact definably normal definable C^r manifold and 2 ≤ r <∞. 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.

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