Consider the set U = {fe Co (R)| limo f(x) = 0}. That is, U is the set of all continuous functions that go to zero as x goes to infinity. Is U a vector space? Check ALL 10 AXIOMS and clearly show which axioms U satisfies and which it does not. Then conclude whether or not U is a vector space. Include every step, if you ever ask yourself "should I also include this??" the answer is YES. Your solution must be clear, complete, and detailed. Hint: U is a set of functions. Don't confuse those functions with their limits.

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