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

Feng, Chunrong; Li, Liangpan

doi:10.1007/s43036-021-00170-1

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

Feng, Chunrong; Li, Liangpan

Authors

Dr Chunrong Feng chunrong.feng@durham.ac.uk
Associate Professor

Liangpan Li

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

Files

Accepted Journal Article (277 Kb)
PDF

Copyright Statement
This is a post-peer-review, pre-copyedit version of a journal article published in Advances in Operator Theory. The final authenticated version is available online at: https://doi.org/10.1007/s43036-021-00170-1