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

Feng, Chunrong and Li, Liangpan (2022) 'Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces.', Advances in Operator Theory, 7 . p. 5.

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.

Item Type:Article
Full text:Publisher-imposed embargo until 03 November 2022.
(AM) Accepted Manuscript
File format - PDF
(271Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s43036-021-00170-1
Publisher 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
Date accepted:17 October 2021
Date deposited:15 November 2021
Date of first online publication:03 November 2021
Date first made open access:03 November 2022

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