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

2021/04/05 by Chunrong Feng, Feng, Chunrong, Liangpan Li +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2104.01827

openalex publication_date 2021/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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