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Journal of Convex Analysis 27 (2020), No. 1, 277--284
Copyright Heldermann Verlag 2020

On the Homotopical Stability of Isolated Critical Points of Continuous Functions

Jean-Noel Corvellec
LAMPS, Université de Perpignan, 66860 Perpignan, France

In the framework of the metric critical point theory, we prove a stability property of the critical groups, for a family of continuous functions which, in a common neighborhood of their respective unique critical point, satisfies a uniform Palais-Smale type condition and is continuous in the uniform topology.

Keywords: Metric Morse theory, continuous functions, critical groups.

MSC: 58E05.

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