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

Autor:	Liangpan Li, Chunrong Feng
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Pure mathematics Algebra and Number Theory FOS: Mathematics Differentiable function Operator theory Analysis Mathematics Counterexample Separable space Functional Analysis (math.FA)
Zdroj:	Advances in Operator Theory, 2022, Vol.7, pp.5 [Peer Reviewed Journal]
DOI:	10.48550/arxiv.2104.01827
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9848bb1754cee09104d5dfaaa5643f5a Zobrazit plný text záznamu