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Interior of a Set

  1. Feb 12, 2010 #1
    I have to describe the interior of the subsets of R: Z,Q.

    I don't understand how to tell if these certain subsets are open or how to tell what the interior is, can someone please explain
     
  2. jcsd
  3. Feb 12, 2010 #2
    Are you working with the standard open-ball topology on the real line?

    If so, then a point [itex]p \in S \subset \mathbb{R}[/itex] is an interior point of S if for some [itex]\epsilon >0[/itex], the open interval [itex](p-\epsilon, p+\epsilon)[/itex] lies completely inside. In other words, a point is an interior point if it lies in the set and is not a boundary point of the set.

    For example, 2 is an interior point of [1,4], but 1 is not an interior point (on the boundary) and neither is 0 (not in the set).

    What happens when you draw a small open interval around a rational number? Will that interval lie completely inside the rational numbers, or does it contain an irrational number?
     
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