What does the notation f|A mean?

  • Thread starter pellman
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666
2
Here is an instance of the notation in context.

If [tex]U_\lambda = F_\lambda(U_0)[/tex] and [tex]U_\lambda\cap U_0\neq\emptyset[/tex], then [tex]F_\lambda |U_{-\lambda}\cap U_0 :U_{-\lambda}\cap U_0 \rightarrow U_0 \cap U_\lambda [/tex] is a diffeomorphism and its inverse is [tex]F_{-\lambda}|U_0 \cap U_\lambda[/tex].

So what does the notation [tex]f|A[/tex] in [tex]f|A:A\rightarrow B[/tex] (where f is a function and A and B are sets) mean?
 

Office_Shredder

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It's usually written f|A as a subscript; it means f with its domain restricted to only A. While you don't have the original definition up, obviously the original domain of F in your statement was U0 (or some superset thereof) and now they're looking at F restricted to the intersection with U-lambda
 
666
2
That fits the other instances of its usage in the text. Thank you.
 

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