A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Let R be endowed with the usual standard topology. Consider Y = [-1,1] as a subspace of R. Which one of the following sets is closed in Y?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    {x: \frac{1}{2}\ < |x| < 1}

  2. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    First, let us talk about what an open set will look like.

  3. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    An open set in the subspace, will be of the form \(A\cap [-1,1]\) where \(A\) is open in \(\mathbb{R}\).

  4. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Every open set in \(\mathbb{R}\) can be written as the union of intervals of the form \((a, b)\).

  5. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Can this be written in the form \(A\cap [-1,1]\) where \(A\) is open in \(\mathbb{R}\)? If so, show me. If not, why not?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    please wait let me think

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes , it can be written like that

  8. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Show me.

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[(-1,1/2) \cup(1/2,1)\]

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so that the union =(-1,1)

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @zzr0ck3r

  12. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I think you mean the following: Consider \((-1, -1/2)\cup (1/2, 1)\). Since \((-1, -1/2)\cup (1/2, 1)\) is open in \(\mathbb{R}\) we have that \([-1,1]\cap[(-1, -1/2)\cup (1/2, 1)]\) is open in the subspace \([-1,1]\)

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes but please explain this \[[−1,1]∩[(−1,−1/2)∪(1/2/1)] \]

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i know that [−1,1]∩[(−1,−1/2)∪(1/2,1)] is open in R

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but i know that [-1,1] is close in R.

  16. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    and in the subspace. because it can be written in the form of [-1,1] intersected with an open set in R

  17. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    This one is sort of trivial, because it is a subset of [-1,1] so it equals the intersection of itself and [-1,1]. Since it was open in R to begin with, it is open in the subspace.

  18. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I really think if you ask about one of the other options, this one will make more sense...

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok but do you have any examples to make me understand more?

  20. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Didn't they give you more options? like I think \[\{x\mid \frac{1}{2}\le |x| < 1\}\] Was this not an option?

  21. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    and \(\{x\mid \frac{1}{2}< |x| \le 1\}\) and \(\{x\mid \frac{1}{2}\le |x| \le 1\}\)

  22. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You here man? These are yes or no questions :)

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    YES THEY DID.

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    NETWORK IS TOOOOOO POOR

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OK, NOW it means that the option that is close is \[{{x∣1/2≤|x|≤1} } \] is the close set. ?

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, with same options, which of them are open in the standard topology on R and which of them are close?

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my guess is that [1/2, 1] is close in R and (1/2,1} is open in R. am i right ? what then will [1/2, 1) and (1/2,1] be . open or close ? please explain

  28. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Are you asked if they are open, or closed. A set can be neither open nor closed. A set can be both open and closed.

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which of the options are open in r and which are close in R and which are nither open or close and which are both open and close in the options above ?

  30. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It does not help you at all for me just to tell you. You need to go with the definition and figure it out. Then it will always make sense.

  31. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Which one would you like to look at?

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[{x∣1/2<|x|≤1} \] this one first, is it open or close in R . i guess it is neither

  33. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Try and write that set as the union of open intervals.

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    will it be \[(-1,-\frac{ 1 }{ 2})\cup(\frac{ 1 }{ 2 },1]\]

  35. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    am i right sir?

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which book or site can i lean how to do this sir?

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i thick it can not be written

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @zzr0ck3r

  39. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \([-1,-\frac{ 1 }{ 2})\cup(\frac{ 1 }{ 2 },1]\)

  40. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The book I gave you covers this in detail.

  41. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Answer this please \([(-2,\dfrac{-1}{2})\cup(\dfrac{1}{2},2)]\cap[-1,1]= \ ?\)

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i have only learnt open sets, close sets, neither open or close , . but i saw an example like that but it only stated the open and the close sets

  43. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Just answer the last question I asked

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer to that question you asked is (-1,1)

  45. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    not at all. You really need to go spend some time learning basic set theory, else there is no way you will learn this. How do we know a set is open in a subspace topology?

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i have not studied sub base sir

  47. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am confuse

  48. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I have said about 5 times the answer to that question. This lets me know that you are not really studying anything I say.

  49. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    at first i thought the answer to that your question is empty set but i was not sure

  50. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You are just guessing and repeating things.... you are not learning The fact that you cant write \(\{x\mid \frac{1}{2}<|x|\le 1\}\) in interval notation tells me that you are very far from being ready for this.

  51. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I am not trying to be rude, but it is a waste of time.

  52. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It took me months to learn what you are trying to brush over in 20 mins, it will not work, you will not pass the test with this method. I gave you a book, and it has problems in it. You should read the book and do the problems, that is the ONLY way to learn math. You may ask me any question you want, but I tell you now that you are wasting your time.

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you sir

  54. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    If you want to keep on with this question, then scroll up and find out where I answerd the following question: How do we know a set is open in a subspace topology? Find the answer and explain what I said. Then we will continue

  55. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i will do that. let me try to learn that, only that i am confuse because the first question was on [-1,1] but now it said which of the options is open in R

  56. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    we are talking about the first question.

  57. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    or at least I am.

  58. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohh. i thought we have answered the first question

  59. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok Close this and ask the new question :)

  60. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.