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A proof of Morse’s theorem about the cancellation of critical points. (English. Abridged French version) Zbl 1279.57023
Summary: In this Note, we give a proof of the famous theorem of M. Morse dealing with the cancellation of a pair of non-degenerate critical points of a smooth function. Our proof consists of a reduction to the one-dimensional case where the question becomes easy to answer.

57R70 Critical points and critical submanifolds in differential topology
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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