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I'm a bit confused as to how the text

The authors define the term

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If A is a set, we denote by

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The authors define the term

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If

**Tensor Analysis on Manifolds**, by Bishop and Goldberg on page 6.The authors define the term

*power set*as follows_________________________________________

If A is a set, we denote by

*P*A the collection of all subsets of A,*P*A = {C| C is a subset of A}.*P*A is called the*power set*of A._________________________________________

The authors define the term

*power map*as follows_________________________________________

If

*f*: A -> B, the we define the*power map*of*f*,*f*:*P*A ->*P*B by*f*C = {*f**c|*

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What is confusing to me is that nowhere in the definition does the set B occur. What role does B have in the power map?

Thank you

Pete*f*a is an element of C} for every C which is an element of*P*A}_________________________________________

What is confusing to me is that nowhere in the definition does the set B occur. What role does B have in the power map?

Thank you

Pete

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