This research proves the openness and density of equivariant definable Morse functions in a specific function set, indicating important properties of these mathematical structures.
Let G be a compact definable C r group, X a compact affine definable C r G manifold and 2 ≤ r < ∞.We prove that the set of equivariant definable Morse functions on X whose loci are finite unions of nondegenerate critical orbits is open and dense in the set of G invariant definable C r functions with respect to the definable C r topology.
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Tomohiro KAWAKAMI (2013) studied this question.
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