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Open and closed

  1. May 27, 2010 #1
    consider (ℝ,τ) , where τ={∅}∪{u⊆ℝ:{-π,π}⊆u}.
    Is [-4.4] open in (ℝ,τ) ? Justify your answer
    Is (-3,3) closed in (ℝ,τ) ? Justify your answer
     
  2. jcsd
  3. May 27, 2010 #2
    Consider [-4,4] ... what do you think the answer should be? What is the definition of "open"? Does this set meet that definition?
     
  4. May 27, 2010 #3

    HallsofIvy

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    What does this mean: "{-π,π}⊆u"? What is "π"? Does this simply mean that U is in the topology if and only if any time x is in U, -x is also? In that case, these questions are close to trivial!

     
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