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Metric spaces

  1. Jan 23, 2008 #1
    Hi there

    I have a proof that I need to try to work out but I'm not really getting too far and need help if you could at all. The question is

    Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+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
    Let h:[0,1]→R be the function given by h(x)= 6x and Let k:[0,1]→R be the function given by k(x)=2+x/2. Is h Є B? Is k Є B?

    Any help at all would be so great
  2. jcsd
  3. Jan 23, 2008 #2
    B = region between the parabolas y=x^2+5 and y=x^2+3 and region between the parobolas y=x^2+1 and y=x^2-1. Draw a picture.
  4. Jan 23, 2008 #3
    I'll try that and see how I get on then. Thanks so much for your suggestion.

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