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Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces. (English) Zbl 1490.46075

Summary: Saint Raymond asked whether continuously differentiable maps with isolated critical points are necessarily open in infinite dimensional (Hilbert) spaces [J. Saint Raymond, Matematiche 71, No. 2, 203–214 (2016; Zbl 1370.46051)]. We answer this question negatively by constructing counterexamples in various settings including all weakly separable spaces.

MSC:

46T20 Continuous and differentiable maps in nonlinear functional analysis

Citations:

Zbl 1370.46051
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References:

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