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shevron

please help with complete matric

  • one year ago
  • one year ago

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  1. shevron
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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

    • one year ago
  2. shevron
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    please help @ timo86m

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

    • one year ago
  4. shevron
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    @timo86m

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

    • one year ago
  6. shevron
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    @Chlorophyll

    • one year ago
  7. shevron
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    @charliem07

    • one year ago
  8. charliem07
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    sorry i dont know

    • one year ago
  9. shevron
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    ok cool

    • one year ago
  10. shevron
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    @Chlorophyll please help

    • one year ago
  11. shevron
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    @hartnn please help

    • one year ago
  12. shevron
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    @UnkleRhaukus please help

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

    • one year ago
  14. shevron
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    @TuringTest please help

    • one year ago
  15. TuringTest
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    @KingGeorge

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

    • one year ago
  17. shevron
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    k thanx

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

    • one year ago
  19. satellite73
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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

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

    • one year ago
  21. satellite73
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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

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

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

    • one year ago
  24. satellite73
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    yes

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

    • one year ago
  26. shevron
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    @Mertsj

    • one year ago
  27. shevron
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    @ash2326

    • one year ago
  28. shevron
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    @walters

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

    • one year ago
  30. phi
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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.

    • one year ago
  31. shevron
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    ok cool

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

    • one year ago
  33. shevron
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    @dmezzullo please help

    • one year ago
  34. shevron
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    @mathslover please help

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

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

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

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

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

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

    • one year ago
  41. mathslover
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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

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

    • one year ago
  43. shevron
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    ok thanx

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

    • one year ago
  45. shevron
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    ok i will

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

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

    • one year ago
  48. shevron
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    @Luis_Rivera please help

    • one year ago
  49. shevron
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    @Agent_Sniffles

    • one year ago
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