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Sequences and nets

  1. Jan 5, 2011 #1
    Say the real numbers were given a topology [tex]\left\{R,\phi, [0,1]\right\}[/tex]. Does the sequence (1/n) converge to every point of [0,1] since it is a neighborhood of every point?
    Last edited: Jan 5, 2011
  2. jcsd
  3. Jan 6, 2011 #2


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    What is [itex]R[/itex] and [itex]\phi[/itex]? Does your topology satisfy the definition of a topology?
  4. Jan 6, 2011 #3


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    If [tex]\mathbb{R}[/tex] has the topology [tex]\{\emptyset,[0,1],\mathbb{R}\}[/tex], then the sequence (1/n) converges to every point of [tex]\mathbb{R}[/tex]!
  5. Jan 6, 2011 #4
    Yeah, I guess you're right. Thanks.
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