Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook