please help with complete matric

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please help with complete matric

Mathematics
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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
please help @ timo86m
sorry idk this one :(

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

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