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Math Help - Topology Open/Closed Sets

  1. #1
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    Topology Open/Closed Sets

    Hey there, I don't know if anyone can help with this or not but what the heck.
    Y=(1,5]. Which of the following subsets of Y are open and which are closed in Y, in the standard topology?

    (0,1), (0,1], [1,2]

    Thanks

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  2. #2
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    Quote Originally Posted by reagan3nc View Post
    Hey there, I don't know if anyone can help with this or not but what the heck.
    Y=(1,5]. Which of the following subsets of Y are open and which are closed in Y, in the standard topology?

    (0,1), (0,1], [1,2]

    Thanks

    None of these sets are subsets of Y! Did you mean Y = (0, 5] ?

    -Dan
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  3. #3
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    Yes I meant Y=(0,5] thanks for catching that.
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  4. #4
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    The only open interval of real numbers have one of these forms: \left( { - \infty ,a} \right),\quad \left( {a,b} \right)\quad or\quad \left( {b,\infty } \right)
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Plato View Post
    The only open interval of real numbers have one of these forms: \left( { - \infty ,a} \right),\quad \left( {a,b} \right)\quad or\quad \left( {b,\infty } \right)
    now here's one of those things that confuse me to no end in topology. (i never took topology officially, and the text i have is like a crash course in topology, so it's not good to learn from). but anyway, somewhere in the text they said [0,1] was an open set

    here's the context:

    they were considering the subspace X = [0,1] \cup (2,3) \subset \mathbb{R}. The claim was, this subspace is not connected since we can express it as the union of two dis-joint, open sets, namely [0,1] and (2,3). Now instead of explaining to a dunce like me why [0,1] is open in the topology of X, the book simply warns, "remember, folks, we're dealing with a topology of X and not that of \mathbb{R}! \cdots"

    i tried looking back through the text to see what the author had said to make him believe this should not be a surprise to me...to no avail.

    the best i could come up with is the definition, "Let X be a topological space. The set A \subset X is called closed when X \backslash A is open"

    now i could not reconcile this with the claim [0,1] is open. is not X \backslash [0,1] = (2,3), which is open, so [0,1] should be closed?
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