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Can you expand a bit on this?

Zero set of a smooth function: Name/Reference

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The part on differential geometry contains the sentence "An unrelated but important result in analysis and geometry states that any closed subset of Rn is the zero set of a smooth function". Does this theorem have a name? Is there any reference describing this theorem? Nahabedere (talk) 13:09, 22 February 2016 (UTC)[reply]

Assessment comment

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The comment(s) below were originally left at Talk:Zero set/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

This should be expanded to include zero sets of polynomials, smooth maps etc. etc. Geometry guy 18:19, 2 June 2007 (UTC)[reply]

Last edited at 18:19, 2 June 2007 (UTC). Substituted at 02:42, 5 May 2016 (UTC)