Functional Analysis by Piotr Hajłasz
= Functional Analysis by Piotr Hajłasz
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{tag=Work by Piotr Hajłasz}
Author-hosted notes: https://sites.pitt.edu/~hajlasz/Notatki/Functional%20Analysis2.pdf
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.