1. 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

2. anonymous

3. anonymous

sorry idk this one :(

4. anonymous

@timo86m

5. anonymous

6. anonymous

@Chlorophyll

7. anonymous

@charliem07

8. anonymous

sorry i dont know

9. anonymous

ok cool

10. anonymous

11. anonymous

12. anonymous

13. UnkleRhaukus

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

14. anonymous

15. TuringTest

@KingGeorge

16. TuringTest

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

17. anonymous

k thanx

18. anonymous

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

19. anonymous

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

20. anonymous

this should work because the metric is the supremum over all $$x$$

21. 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

22. anonymous

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

23. anonymous

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

24. anonymous

yes

25. anonymous

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

26. anonymous

@Mertsj

27. anonymous

@ash2326

28. anonymous

@walters

29. anonymous

30. phi

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

31. anonymous

ok cool

32. anonymous

can u fynd me someone who can do it

33. anonymous

34. anonymous

35. mathslover

Sorry, am not good at this topic.

36. anonymous

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

37. mathslover

Yes! I am best at that field :)

38. anonymous

39. mathslover

40. anonymous

eish they blocked youtube here at school

41. mathslover
42. mathslover
43. anonymous

ok thanx

44. mathslover

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

45. anonymous

ok i will

46. anonymous

@mathslover they are not helping

47. mathslover
48. anonymous