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

Feng, Chunrong; Li, Liangpan

Abstract

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 including all weakly separable spaces.

Citation

Feng, C., & Li, L. (2022). Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces. Advances in operator theory, 7, Article 5. https://doi.org/10.1007/s43036-021-00170-1

• Journal Article Type: Article
• Acceptance Date: Oct 17, 2021
• Online Publication Date: Nov 3, 2021
• Publication Date: 2022
• Deposit Date: Nov 14, 2021
• Publicly Available Date: Nov 3, 2022
• Journal: Advances in Operator Theory
• Electronic ISSN: 2538-225X
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Article Number: 5
• DOI: https://doi.org/10.1007/s43036-021-00170-1
• Public URL: https://durham-repository.worktribe.com/output/1225041