shevron
please help with complete matric
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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
shevron
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please help @ timo86m
timo86m
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sorry idk this one :(
shevron
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@timo86m
shevron
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@Callisto ,@Chlorophyll ,@charliem07 please help
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@Chlorophyll
shevron
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@charliem07
charliem07
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sorry i dont know
shevron
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ok cool
shevron
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@Chlorophyll please help
shevron
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@hartnn please help
shevron
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@UnkleRhaukus please help
UnkleRhaukus
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@JamesJ, @experimentX, @eliassaab, @nbouscal, @beketso
shevron
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@TuringTest please help
TuringTest
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@KingGeorge
shevron
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k thanx
anonymous
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your job is showing it is "complete" is to show that if \(f_n\to f\) then \(f\in C_b\)
anonymous
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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
anonymous
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this should work because the metric is the supremum over all \(x\)
anonymous
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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
shevron
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do i have to let the sequence to be a cauchy sequence first?
anonymous
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actually what i meant is the uniform limit of a sequence of continuous functions is CONTINUOUS
anonymous
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yes
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
shevron
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@Mertsj
shevron
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@ash2326
shevron
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@walters
shevron
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@phi please help me
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.
shevron
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ok cool
shevron
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can u fynd me someone who can do it
shevron
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@dmezzullo please help
shevron
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@mathslover please help
mathslover
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Sorry, am not good at this topic.
shevron
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ok can you search for me where i can find something related to ths?
mathslover
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Yes! I am best at that field :)
shevron
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lol i will be glad
shevron
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eish they blocked youtube here at school
shevron
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ok thanx
mathslover
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Have a look at the links and let me know whether they helped or not.
shevron
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ok i will
shevron
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@mathslover they are not helping
shevron
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@Luis_Rivera please help
shevron
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@Agent_Sniffles