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Open and Closed Sets

  1. Oct 10, 2013 #1
    Prove that for any collection {Oα} of open subsets of ℝ, [itex]\bigcap[/itex] Oα is open.


    I did the following for the union, but I don't see where to go with the intersection of a set.

    Here's what I have so far:

    Suppose Oα is an open set for each x [itex]\ni[/itex] A. Let O= [itex]\bigcap[/itex] Oα. Consider an arbitrary x in O. By definition of O, x is in O, and O is open by hypothesis. So x is an interior point of Oα
     
    Last edited: Oct 10, 2013
  2. jcsd
  3. Oct 10, 2013 #2

    LCKurtz

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    What if ##O_n = (-\frac 1 n, \frac 1 n)##?
     
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