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Convergent sequences in the cofinite topology

  1. Apr 18, 2012 #1
    How can you identify the class of all sequences that converge in the cofinite topology and to what they converge to? I get the idea that any sequence that doesn't oscillate between two numbers can converge to something in the cofinite topology. Considering a constant sequence converges to the constant, a divergent sequence to +- infinity converges to all points, a sequence that gets infinitely closer to a number converges. Am I essentially on the right track here or can anyone give me a counterexample to my claim?
  2. jcsd
  3. Apr 18, 2012 #2
    Try to differentiate between:

    The sequence takes on a finite number of values


    The sequence takes on an infinite number of values.
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