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    Is [0,1] Closed at the Origin?

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    Please solve the following problem:

    Let C ([0,1]) be the space of continuous functions in [0,1] with the norm
    II f II = max I f(x) I on [0,1].
    Is the subspace of functions that are = 0 at the origin closed subspace in
    C^0 [o,1] with this norm/Prove or disapprove.

    © BrainMass Inc. brainmass.com December 15, 2020, 7:05 pm ad1c9bdddf

    Solution Preview

    Yes, it is closed. Suppose, {f_n} is a sequence of functions from the subspace Y={g in C([0,1]): g(0)=0} converging to some function f in C([0,1]) in ...

    Solution Summary

    The solution proves or disapproves if [0,1] closed at the origin.