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Let $X$ be a closed manifold, let $k$ be a nonnegative integer and let $C^k(X)$ denote the space of $k$-times continuously differentiable functions equipped with the C$^k$ norm.

Is $C^{k+1}(X)$ compactly contained in $C^k(X)$? Does this follow from Arzela-Ascoli?

Thanks.

  • 0
    **TIP**: You can also use $\LaTeX$ in titles!2012-09-01
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    great! thanks for letting me know2012-09-01
  • 0
    Is being [compactly embedded](http://en.wikipedia.org/wiki/Compactly_embedded) the same as compact containment?2012-09-01
  • 0
    [Asked and answered on MO](http://mathoverflow.net/questions/106081/).2012-09-01

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