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Math Help - Sets

  1. #1
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    Sets

    Let S and T be subsets of R. Prove the Following:

    A) int(int S) = int S

    for this one do I just need to take the set S, and show that the interiors interior is still part of the interior?


    B) int(S \cap T) = (int S) \cap (int T)

    For this one do I just assume there is some x \in int(S \cap T) and follow from there?
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  2. #2
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    This is all about open sets.
    The interior of a set is an open set: it is the union of open sets.
    So surely \text{int}(\text{int}(S))=\text{int}(S)
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  3. #3
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    Quote Originally Posted by Plato View Post
    This is all about open sets.
    The interior of a set is an open set: it is the union of open sets.
    So surely \text{int}(\text{int}(S))=\text{int}(S)
    ohh i see.

    I have a whole section with questions similar to these for homework.
    I wasnt quite sure how to approach them.


    thanks
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