Quick Question about Smooth Maps

  • Thread starter slevvio
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  • #1
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Hello everyone, I just had a quick question I was hoping somebody could answer.

If [itex]f: M \times N \rightarrow P[/itex] is a smooth map, where [itex]M,N[/itex] and [itex]P[/itex] are smooth manifolds, then is it true for fixed [itex]m[/itex] that [itex]f_m : N \rightarrow P[/itex] is smooth, where [itex]f_m (n) = f(m,n)[/itex]?

Any help would be appreciated.
 

Answers and Replies

  • #2
quasar987
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Of course, since the equivalent statement when M=R^m, N=R^n is true.
 
  • #3
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ok thank you!
 

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