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shevron
 one year ago
Best ResponseYou've already chosen the best response.0let \[\left( X;d \right)\] 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
 one year ago
Best ResponseYou've already chosen the best response.0@Callisto ,@Chlorophyll ,@charliem07 please help

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@Chlorophyll please help

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus please help

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0@JamesJ, @experimentX, @eliassaab, @nbouscal, @beketso

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@TuringTest please help

TuringTest
 one year ago
Best ResponseYou've already chosen the best response.0btw for advanced questions you may have better luck here http://math.stackexchange.com/

satellite73
 one year ago
Best ResponseYou've already chosen the best response.3your job is showing it is "complete" is to show that if \(f_n\to f\) then \(f\in C_b\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.3that is, if a sequence of continuous functions converges to some function using the sup metric, then the limit function is continuous also

satellite73
 one year ago
Best ResponseYou've already chosen the best response.3this should work because the metric is the supremum over all \(x\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.3the 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
 one year ago
Best ResponseYou've already chosen the best response.0do i have to let the sequence to be a cauchy sequence first?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.3actually what i meant is the uniform limit of a sequence of continuous functions is CONTINUOUS

shevron
 one year ago
Best ResponseYou've already chosen the best response.0my problem we are given f and g and they are different how am i going to proof them simultaneously

phi
 one year ago
Best ResponseYou've already chosen the best response.0I assume you mean "metric space" ? But I tend more to applied math problems. i.e. not this kind of question.

shevron
 one year ago
Best ResponseYou've already chosen the best response.0can u fynd me someone who can do it

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@dmezzullo please help

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@mathslover please help

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, am not good at this topic.

shevron
 one year ago
Best ResponseYou've already chosen the best response.0ok can you search for me where i can find something related to ths?

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Yes! I am best at that field :)

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1https://www.youtube.com/watch?v=04pvLCDbq1c ^ a video tutorial

shevron
 one year ago
Best ResponseYou've already chosen the best response.0eish they blocked youtube here at school

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1That'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/metricspace

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1oh forgot this : http://wwwhistory.mcs.stand.ac.uk/~john/analysis/Lectures/L15.html

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Have a look at the links and let me know whether they helped or not.

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@mathslover they are not helping

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1http://www.wiziq.com/tutorial/88701ProblemsinMetricSpaces1 Check it out

shevron
 one year ago
Best ResponseYou've already chosen the best response.0@Luis_Rivera please help
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