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anonymous

  • one year ago

Let X=(a,b,c,d,e)andτ=(X,ϕ,[a],[c,d],[a,c,d],[b,c,d,e]).LetA=[a,c] , then set A′of limit points of A is given by

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  1. anonymous
    • one year ago
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    A′=(b,c,e) A′=(b,d,e) A′=(b,e) A′=X

  2. anonymous
    • one year ago
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    @zzr0ck3r

  3. anonymous
    • one year ago
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    i think option B

  4. anonymous
    • one year ago
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    @zzr0ck3r

  5. anonymous
    • one year ago
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    am i correct ?

  6. zzr0ck3r
    • one year ago
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    Do you mean interval [ ] ?

  7. zzr0ck3r
    • one year ago
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    or { }

  8. zzr0ck3r
    • one year ago
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    do you mean the empty set \(\emptyset\) and not that weird thing?

  9. anonymous
    • one year ago
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    i think {} and that weird thing is empty set

  10. zzr0ck3r
    • one year ago
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    ok can you edit it to make sense?

  11. zzr0ck3r
    • one year ago
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    these things mean different things...

  12. anonymous
    • one year ago
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    X=(a,b,c,d,e)andτ=(X,ϕ,{a},{c,d},{a,c,d},{b,c,d,e}).LetA={a,c} , then set A′ of limit points of A is given by

  13. anonymous
    • one year ago
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    @zzr0ck3r

  14. zzr0ck3r
    • one year ago
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    why do you think B?

  15. anonymous
    • one year ago
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    because that is A complement with X

  16. zzr0ck3r
    • one year ago
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    So you think that the set of limit points is defined to be the compliment?

  17. anonymous
    • one year ago
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    please i will be happy if you explain the concept with you

  18. zzr0ck3r
    • one year ago
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    I already have.

  19. zzr0ck3r
    • one year ago
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    What is a limit point?

  20. anonymous
    • one year ago
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    it is the boundary points or closed interval points

  21. anonymous
    • one year ago
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    @zzr0ck3r

  22. zzr0ck3r
    • one year ago
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    So you did not read a thing I wrote on the last problem?

  23. zzr0ck3r
    • one year ago
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    Go back and read that and then tell me what a limit point is

  24. anonymous
    • one year ago
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    a point for which every neighborhood contains at least one point belonging to a given set.

  25. zzr0ck3r
    • one year ago
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    Also, when you reply to something I have commented on, I get tagged and see it. There is no reason to tag me more than once on a post.

  26. zzr0ck3r
    • one year ago
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    ok, so what are the open sets containing b?

  27. anonymous
    • one year ago
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    ,{b,c,d,e}

  28. zzr0ck3r
    • one year ago
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    does that intersect A? in other words, does that share any points with A?

  29. anonymous
    • one year ago
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    yes c

  30. zzr0ck3r
    • one year ago
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    ok, what are the open sets containing d?

  31. anonymous
    • one year ago
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    {c,d},{a,c,d},{b,c,d,e}

  32. zzr0ck3r
    • one year ago
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    I shuold be saying intersect A at some other point...

  33. zzr0ck3r
    • one year ago
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    ok do all of those sets intersect A at some other point other than d?

  34. zzr0ck3r
    • one year ago
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    why are you using caps?

  35. zzr0ck3r
    • one year ago
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    d is not in A... try again

  36. anonymous
    • one year ago
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    sorry . 'a' for the first and 'c' for the second and third

  37. zzr0ck3r
    • one year ago
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    right

  38. zzr0ck3r
    • one year ago
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    ok and with e we get the same thing as with b right?

  39. anonymous
    • one year ago
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    yes

  40. zzr0ck3r
    • one year ago
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    So your option is looking good, but maybe some other point is also a limit point. What open sets contain a?

  41. zzr0ck3r
    • one year ago
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    Better yet, do all of the open sets that contain a also intersect A at some point other than a?

  42. anonymous
    • one year ago
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    {a},{a,c,d}

  43. zzr0ck3r
    • one year ago
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    do all of the open sets that contain a also intersect A at some point other than a?

  44. anonymous
    • one year ago
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    yes

  45. anonymous
    • one year ago
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    but not {a}

  46. zzr0ck3r
    • one year ago
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    right so you mean no then?

  47. anonymous
    • one year ago
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    yes

  48. zzr0ck3r
    • one year ago
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    then a is not a limit point what about c?

  49. zzr0ck3r
    • one year ago
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    is c a limit point?

  50. anonymous
    • one year ago
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    yes ,{a,c,d} because it intersects A

  51. zzr0ck3r
    • one year ago
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    is that the only open set that contains c? Remember, we only have to find one that does not intersect at some point other than c

  52. anonymous
    • one year ago
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    ,{c,d},{a,c,d},{b,c,d,e} contain c

  53. zzr0ck3r
    • one year ago
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    do all of those intersect A at some point different than c?

  54. anonymous
    • one year ago
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    only {a,c,d}

  55. zzr0ck3r
    • one year ago
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    so there is at least one that does not?

  56. zzr0ck3r
    • one year ago
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    then c is NOT a limit point. So yes your option B is the answer, but not for the reason you listed :)

  57. anonymous
    • one year ago
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    ok. thanks . i have to view this page more often to understand this

  58. anonymous
    • one year ago
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    Let A=(0,1]⋃2 be a subset of R

  59. anonymous
    • one year ago
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    what are the limit points

  60. zzr0ck3r
    • one year ago
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    remember to show something is not a limit points you need to show that it has an open set around it that intersects the set at some point OTHER than the point in question. I did not stress that in the last post.

  61. anonymous
    • one year ago
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    ok thanks

  62. zzr0ck3r
    • one year ago
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    For a subset \(A\subset X\) a limit point \(x\) of \(A\) is a point in \(X\) (not necessarily in \(A\)) such that all open sets containing it intersect \(A\) at some point other than \(x\).

  63. anonymous
    • one year ago
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    i think 0 and 1

  64. anonymous
    • one year ago
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    ok

  65. zzr0ck3r
    • one year ago
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    you think what 0 and 1?

  66. anonymous
    • one year ago
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    Let A=(0,1]⋃2 be a subset of R

  67. zzr0ck3r
    • one year ago
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    done

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