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Convergence of sequences in topological spaces?

  1. Sep 16, 2009 #1
    hi
    I was having difficulty with this problem in the book

    If (1/n) is a sequence in R

    which points (if any) will it converge (for every open set there is an integer N such that for all n>N 1/n is in that open set) to using the following topologies

    (a) Discrete
    (b) Indiscrete
    (c) { A in X : A\X is countable or all of X }

    For indiscrete I know that any sequence will converge to any point in R

    For discrete -the sequence doesnt coverge to any points

    and for (c) Im thinking the sequence again doesnt converge to any points

    but im not sure how to prove the last ones ...or if theyre even right

    any help?
     
  2. jcsd
  3. Sep 16, 2009 #2

    Office_Shredder

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    What do you mean by A\X? Most people write set theoretic subtraction as X\A (since A is a subset of X, you can't subtract X from A meaningfully), is that your intent?
     
  4. Sep 16, 2009 #3
    yea thats what i meant, sorry -)
     
  5. Sep 16, 2009 #4
    i dont really require a proof - i just want to know if i got the right answers
    that is discrete topology -no point of convergence
    indiscrete -all points are points of convergence
    and the last one -no point is a point of convergence

    thanks
     
  6. Sep 17, 2009 #5
    Yes, those answers are correct to the best of my knowledge.
     
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