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Differential Forms. Suppose U is an open subset of Rn
 

Summary: Differential Forms.
Suppose U is an open subset of Rn
.
Defintion. For each nonnegative integer p we let
Ap
(U)
be the set of smooth maps
: U
p
Rn
.
Note that Ap
(U) is a vector space in a natural way. Whenever f is a smooth real valued function on U and
Ap
(U) we define f in Ap
(U) by setting f(x) = f(x)(x) for x in U.
Proposition. There is one and only one bilinear map from
W : L(
1
Rn

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics