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I Interior and closure in non-Euclidean topology

  1. Jan 29, 2017 #1
    Hello everyone,

    I was wondering if someone could assist me with the following problem:

    Let T be the topology on R generated by the topological basis B:
    B = {{0}, (a,b], [c,d)}
    a < b </ 0
    0 </ c < d

    Compute the interior and closure of the set A:
    A = (−3, −2] ∪ (−1, 0) ∪ (0, 1) ∪ (2, 3)

    I understand that in Euclidean topology I would just include/exclude the boundary points but I don't know how to do this with a different topology, especially since I feel that this topological space is very, very similar to the Euclidean topology, I have shown that all opens in that space are open here as well. What do I do?

    Thanks in advance!
     
  2. jcsd
  3. Jan 29, 2017 #2

    Svein

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    Science Advisor

    Do you mean a < b ≤ 0; 0 ≤ c < d?
     
  4. Jan 29, 2017 #3
    Yes!
     
  5. Jan 29, 2017 #4

    Svein

    User Avatar
    Science Advisor

    The the problem must be dealt with in stages:
    1. a < b < -3; 3 < c < d
    2. a < -3, -3 < b <-2; 3 < c < d
    3. etc. etc.
     
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