Question

please help with complete matric

Answer 1

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

Answer 2

please help @ timo86m

Answer 3

sorry idk this one :(

Answer 4

@timo86m

Answer 5

@Callisto ,@Chlorophyll ,@charliem07 please help

Answer 6

@Chlorophyll

Answer 7

@charliem07

Answer 8

sorry i dont know

Answer 9

ok cool

Answer 10

@Chlorophyll please help

Answer 11

@hartnn please help

Answer 12

@UnkleRhaukus please help

Answer 13

@JamesJ, @experimentX, @eliassaab, @nbouscal, @beketso

Answer 14

@TuringTest please help

Answer 15

@KingGeorge

Answer 16

btw for advanced questions you may have better luck here http://math.stackexchange.com/

Answer 17

k thanx

Answer 18

your job is showing it is "complete" is to show that if \(f_n\to f\) then \(f\in C_b\)

Answer 19

that is, if a sequence of continuous functions converges to some function using the sup metric, then the limit function is continuous also

Answer 20

this should work because the metric is the supremum over all \(x\)

Answer 21

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

Answer 22

do i have to let the sequence to be a cauchy sequence first?

Answer 23

actually what i meant is the uniform limit of a sequence of continuous functions is CONTINUOUS

Answer 24

yes

Answer 25

my problem we are given f and g and they are different how am i going to proof them simultaneously

Answer 26

@Mertsj

Answer 27

@ash2326

Answer 28

@walters

Answer 29

@phi please help me

Answer 30

I assume you mean "metric space" ? But I tend more to applied math problems. i.e. not this kind of question.

Answer 31

ok cool

Answer 32

can u fynd me someone who can do it

Answer 33

@dmezzullo please help

Answer 34

@mathslover please help

Answer 35

Sorry, am not good at this topic.

Answer 36

ok can you search for me where i can find something related to ths?

Answer 37

Yes! I am best at that field :)

Answer 38

lol i will be glad

Answer 39

https://www.youtube.com/watch?v=04pvLCDbq1c

^ a video tutorial

Answer 40

eish they blocked youtube here at school

Answer 41

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

Answer 42

oh forgot this : http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L15.html

Answer 43

ok thanx

Answer 44

Have a look at the links and let me know whether they helped or not.

Answer 45

ok i will

Answer 46

@mathslover they are not helping

Answer 47

http://www.wiziq.com/tutorial/88701-Problems-in-Metric-Spaces-1

Check it out

Answer 48

@Luis_Rivera please help

Answer 49

@Agent_Sniffles