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Math Help - topology

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    topology

    Hello all
    Last edited by rolylane; February 10th 2008 at 09:43 AM.
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  2. #2
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    Quote Originally Posted by rolylane View Post
    Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x+2. Let B={g Є C[0,1]: 1 ≤ d(g,f) ≤ 3}
    Describe the region in which the functions in B have their graphs
    The difference between g(x) and f(x) must be between 1 and 3, for all x in the interval. What's more, g is continuous, so it can't be greater than f(x) for some values of x, and less than f(x) for other values of x. So either x^2+3\leqslant g(x)\leqslant 5 for all x in [0,1], or x^2-1\leqslant g(x)\leqslant 1 for all x in [0,1].
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    Thank you so much for your time. I appreciate your help
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