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shevron

  • one year ago

please help with complete matric

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  1. shevron
    • one year ago
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    let \[\left( X;d \right)\] be a matric space and \[C_{b}\]\[\left( X,R \right)\] denote the set of all continuous bounded real valued functions defined on X, equipped with the uniform metric. \[ d\left( f,g \right)=sup{ \left| f \left( x \right)-g \left( x \right) \right|: xinX }\] Show that \[C_{b}\]\[\left( X,R \right)\] is a complete matric space

  2. shevron
    • one year ago
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    please help @ timo86m

  3. timo86m
    • one year ago
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    sorry idk this one :(

  4. shevron
    • one year ago
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    @timo86m

  5. shevron
    • one year ago
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    @Callisto ,@Chlorophyll ,@charliem07 please help

  6. shevron
    • one year ago
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    @Chlorophyll

  7. shevron
    • one year ago
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    @charliem07

  8. charliem07
    • one year ago
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    sorry i dont know

  9. shevron
    • one year ago
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    ok cool

  10. shevron
    • one year ago
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    @Chlorophyll please help

  11. shevron
    • one year ago
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    @hartnn please help

  12. shevron
    • one year ago
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    @UnkleRhaukus please help

  13. UnkleRhaukus
    • one year ago
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    @JamesJ, @experimentX, @eliassaab, @nbouscal, @beketso

  14. shevron
    • one year ago
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    @TuringTest please help

  15. TuringTest
    • one year ago
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    @KingGeorge

  16. TuringTest
    • one year ago
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    btw for advanced questions you may have better luck here http://math.stackexchange.com/

  17. shevron
    • one year ago
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    k thanx

  18. satellite73
    • one year ago
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    your job is showing it is "complete" is to show that if \(f_n\to f\) then \(f\in C_b\)

  19. satellite73
    • one year ago
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    that is, if a sequence of continuous functions converges to some function using the sup metric, then the limit function is continuous also

  20. satellite73
    • one year ago
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    this should work because the metric is the supremum over all \(x\)

  21. satellite73
    • one year ago
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    the general idea is that under the sup metric, the convergence is uniform, and the uniform limit of a sequence of continuous functions is uniform gotta run, but if you google what i wrote i bet you will find a worked out solution

  22. shevron
    • one year ago
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    do i have to let the sequence to be a cauchy sequence first?

  23. satellite73
    • one year ago
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    actually what i meant is the uniform limit of a sequence of continuous functions is CONTINUOUS

  24. satellite73
    • one year ago
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    yes

  25. shevron
    • one year ago
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    my problem we are given f and g and they are different how am i going to proof them simultaneously

  26. shevron
    • one year ago
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    @Mertsj

  27. shevron
    • one year ago
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    @ash2326

  28. shevron
    • one year ago
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    @walters

  29. shevron
    • one year ago
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    @phi please help me

  30. phi
    • one year ago
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    I assume you mean "metric space" ? But I tend more to applied math problems. i.e. not this kind of question.

  31. shevron
    • one year ago
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    ok cool

  32. shevron
    • one year ago
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    can u fynd me someone who can do it

  33. shevron
    • one year ago
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    @dmezzullo please help

  34. shevron
    • one year ago
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    @mathslover please help

  35. mathslover
    • one year ago
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    Sorry, am not good at this topic.

  36. shevron
    • one year ago
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    ok can you search for me where i can find something related to ths?

  37. mathslover
    • one year ago
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    Yes! I am best at that field :)

  38. shevron
    • one year ago
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    lol i will be glad

  39. mathslover
    • one year ago
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    https://www.youtube.com/watch?v=04pvLCDbq1c ^ a video tutorial

  40. shevron
    • one year ago
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    eish they blocked youtube here at school

  41. mathslover
    • one year ago
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    That's good decision even :) . http://www.csie.ntnu.edu.tw/~bbailey/metric%20spaces.htm http://www.maths.usyd.edu.au/u/UG/SM/MATH3961/ http://www.wiziq.com/tutorials/metric-space

  42. mathslover
    • one year ago
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    oh forgot this : http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L15.html

  43. shevron
    • one year ago
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    ok thanx

  44. mathslover
    • one year ago
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    Have a look at the links and let me know whether they helped or not.

  45. shevron
    • one year ago
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    ok i will

  46. shevron
    • one year ago
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    @mathslover they are not helping

  47. mathslover
    • one year ago
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    http://www.wiziq.com/tutorial/88701-Problems-in-Metric-Spaces-1 Check it out

  48. shevron
    • one year ago
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    @Luis_Rivera please help

  49. shevron
    • one year ago
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    @Agent_Sniffles

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