anonymous
  • anonymous
please help with complete matric
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
please help @ timo86m
anonymous
  • anonymous
sorry idk this one :(

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anonymous
  • anonymous
@timo86m
anonymous
  • anonymous
@Callisto ,@Chlorophyll ,@charliem07 please help
anonymous
  • anonymous
@Chlorophyll
anonymous
  • anonymous
@charliem07
anonymous
  • anonymous
sorry i dont know
anonymous
  • anonymous
ok cool
anonymous
  • anonymous
@Chlorophyll please help
anonymous
  • anonymous
@hartnn please help
anonymous
  • anonymous
@UnkleRhaukus please help
UnkleRhaukus
  • UnkleRhaukus
@JamesJ, @experimentX, @eliassaab, @nbouscal, @beketso
anonymous
  • anonymous
@TuringTest please help
TuringTest
  • TuringTest
@KingGeorge
TuringTest
  • TuringTest
btw for advanced questions you may have better luck here http://math.stackexchange.com/
anonymous
  • anonymous
k thanx
anonymous
  • anonymous
your job is showing it is "complete" is to show that if \(f_n\to f\) then \(f\in C_b\)
anonymous
  • anonymous
that is, if a sequence of continuous functions converges to some function using the sup metric, then the limit function is continuous also
anonymous
  • anonymous
this should work because the metric is the supremum over all \(x\)
anonymous
  • anonymous
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
anonymous
  • anonymous
do i have to let the sequence to be a cauchy sequence first?
anonymous
  • anonymous
actually what i meant is the uniform limit of a sequence of continuous functions is CONTINUOUS
anonymous
  • anonymous
yes
anonymous
  • anonymous
my problem we are given f and g and they are different how am i going to proof them simultaneously
anonymous
  • anonymous
@Mertsj
anonymous
  • anonymous
@ash2326
anonymous
  • anonymous
@walters
anonymous
  • anonymous
@phi please help me
phi
  • phi
I assume you mean "metric space" ? But I tend more to applied math problems. i.e. not this kind of question.
anonymous
  • anonymous
ok cool
anonymous
  • anonymous
can u fynd me someone who can do it
anonymous
  • anonymous
@dmezzullo please help
anonymous
  • anonymous
@mathslover please help
mathslover
  • mathslover
Sorry, am not good at this topic.
anonymous
  • anonymous
ok can you search for me where i can find something related to ths?
mathslover
  • mathslover
Yes! I am best at that field :)
anonymous
  • anonymous
lol i will be glad
mathslover
  • mathslover
https://www.youtube.com/watch?v=04pvLCDbq1c ^ a video tutorial
anonymous
  • anonymous
eish they blocked youtube here at school
mathslover
  • mathslover
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
mathslover
  • mathslover
oh forgot this : http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L15.html
anonymous
  • anonymous
ok thanx
mathslover
  • mathslover
Have a look at the links and let me know whether they helped or not.
anonymous
  • anonymous
ok i will
anonymous
  • anonymous
@mathslover they are not helping
mathslover
  • mathslover
http://www.wiziq.com/tutorial/88701-Problems-in-Metric-Spaces-1 Check it out
anonymous
  • anonymous
@Luis_Rivera please help
anonymous
  • anonymous
@Agent_Sniffles

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