Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces

Chunrong Feng; Liangpan Li

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arXiv · 2104.01827

Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces

Chunrong Feng·Liangpan Li

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Abstract

Jean Saint Raymond asked whether continuously differentiable maps with isolated critical points are necessarily open in infinite dimensional (Hilbert) spaces. We answer this question negatively by constructing counterexamples in various settings.

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BibTeX RIS

Chunrong Feng, Liangpan Li. 2021-04-05. Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces. https://arxiv.org/abs/2104.01827

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