1. shevron Group Title

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. shevron Group Title

3. timo86m Group Title

sorry idk this one :(

4. shevron Group Title

@timo86m

5. shevron Group Title

6. shevron Group Title

@Chlorophyll

7. shevron Group Title

@charliem07

8. charliem07 Group Title

sorry i dont know

9. shevron Group Title

ok cool

10. shevron Group Title

11. shevron Group Title

12. shevron Group Title

13. UnkleRhaukus Group Title

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

14. shevron Group Title

15. TuringTest Group Title

@KingGeorge

16. TuringTest Group Title

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

17. shevron Group Title

k thanx

18. satellite73 Group Title

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

19. satellite73 Group Title

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

20. satellite73 Group Title

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

21. satellite73 Group Title

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. shevron Group Title

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

23. satellite73 Group Title

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

24. satellite73 Group Title

yes

25. shevron Group Title

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

26. shevron Group Title

@Mertsj

27. shevron Group Title

@ash2326

28. shevron Group Title

@walters

29. shevron Group Title

30. phi Group Title

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

31. shevron Group Title

ok cool

32. shevron Group Title

can u fynd me someone who can do it

33. shevron Group Title

34. shevron Group Title

35. mathslover Group Title

Sorry, am not good at this topic.

36. shevron Group Title

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

37. mathslover Group Title

Yes! I am best at that field :)

38. shevron Group Title

39. mathslover Group Title

40. shevron Group Title

eish they blocked youtube here at school

41. mathslover Group Title
42. mathslover Group Title
43. shevron Group Title

ok thanx

44. mathslover Group Title

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

45. shevron Group Title

ok i will

46. shevron Group Title

@mathslover they are not helping

47. mathslover Group Title
48. shevron Group Title