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Let S be a nonempty set and F a. field. Let C(S, F) denote the set of all functions /

Chapter 1, Problem 14

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QUESTION:

Let S be a nonempty set and F a. field. Let C(S, F) denote the set of all functions / T(S, F) such that f(s) 0 for all but a finite number of elements of S. Prove that C(S, F) is a subspace of ^(S, F

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QUESTION:

Let S be a nonempty set and F a. field. Let C(S, F) denote the set of all functions / T(S, F) such that f(s) 0 for all but a finite number of elements of S. Prove that C(S, F) is a subspace of ^(S, F

ANSWER:

Step 1 of 2

Let  be a vector space and  is a subset of  . is a subspace of   

(a)  

(b)  for

(c)  for and

 

-  

- Let  and  

 is a subspace of  .

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