The distance function to a finite set is a topological Morse function - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

The distance function to a finite set is a topological Morse function

Charles Arnal

Résumé

In this short note, we show that the distance function to any finite set X ⊂ Rn is a topological Morse function, regardless of whether X is in general position. We also precisely characterize its topological critical points and their indices, and relate them to the differential critical points of the function.
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Dates et versions

hal-04657849 , version 1 (22-07-2024)

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  • HAL Id : hal-04657849 , version 1

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Charles Arnal. The distance function to a finite set is a topological Morse function. 2024. ⟨hal-04657849⟩
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