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verify the assertion. (Subspace example) 1) The set of continuous real-valued functions on the interval [0,1] is...

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Advance Math

verify the assertion. (Subspace example)

1) The set of continuous real-valued functions on the interval[0,1] is a subspace of R^[0,1]

This is from Linear Algebra Done Right- Sheldon Axler 3rdedition.

I don't understand why the solution uses a integral.

Answer & Explanation Solved by verified expert
4.3 Ratings (762 Votes)
First note that R01 f f01R and let S f f01R such that f is continuous According to defination you need to show that the set of continuous functions is non empty and that it is closed under the operations of R01 And by the    See Answer
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