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    Finite dimensional linear submanifold of N is complete.

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    Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.

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    Solution Preview

    Please see the attached file.

    Suppose that is a normed linear space.
    Let be a finite dimensional linear submanifold of .
    Hence itself is a finite dimensional normed linear space.

    Now we have to prove that is complete and therefore closed.
    Let B = be a basis for so that
    -------------------------------------(1)
    ...

    Solution Summary

    This solution is comprised of a detailed explanation of the problem on a normed linear space.
    It contains step-by-step explanation for the following problem:
    Normed Linear Space:

    Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold
    of N is complete and therefore closed.

    Solution contains detailed step-by-step explanation.

    $2.49

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