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Restriction Map


For open sets V subset= U and a sheaf F, the restriction map

 rho_(U,V):F(U)->F(V)

sends a section over U to its restriction to V. These maps satisfy rho_(U,U) equal to the identity and rho_(V,W) degreesrho_(U,V)=rho_(U,W) whenever W subset= V subset= U.

For ordinary functions, restriction similarly means replacing a function f:X->Y by the function f|_A:A->Y on a subset A subset= X.


See also

Presheaf, Restriction of a Sheaf, Sheaf, Sheaf Section, Stalk

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Cite this as:

Weisstein, Eric W. "Restriction Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RestrictionMap.html

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