Functional Analysis by Piotr Hajłasz
ID: functional-analysis-by-piotr-hajlasz
Consulted passage: Proposition8.3 and proof, printed pp75–76 (PDF pages75–76, zero-based74–75), showing that a smooth real function with some vanishing derivative at each point is a polynomial. The proof uses the Baire category theorem twice and the perfect closed complement of the locally polynomial locus.
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