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Topology question

  1. Oct 7, 2007 #1
    Suppose I have some subset of R, not necessarily an interval, let it be denoted as A. I have some union (might be countable, might be finite, might be uncountable) of sets where each set is an open set of A and the union of the open sets is equal to A. Can I conclude that A is open?

    I am not sure because the sets are open in A, not necessarily open in R. I don't know much about A other than it is some subset of R.

    Any help?
  2. jcsd
  3. Oct 7, 2007 #2


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    You can't conclude that A is open. For a trivial example, take a non-open subset A of R. Note that A is open in itself.
  4. Oct 7, 2007 #3


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    If all that you know is that the sets are open in A this can't tell you anything about whether A is open in R. E.g. A is always open in A.
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