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