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

Topology on N

  1. Sep 4, 2008 #1
    Hi...I'm new to the forum but I need help with the following question.

    I need to find a topology on N for which there are exactly k limit points. k is a positive integer.

    Tips I have received: find countable subsets in R...then a bijection will produce the needed topology on N?

    Any help is greatly appreciated.
  2. jcsd
  3. Sep 5, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    I'm not sure I understand your question. What does it mean for a topology to only have k limit points?

    Presumably N is the set of natural numbers. Are you trying to consider N as a free-standing topological space, or are you trying to topologize R, and then give N the subspace topology?
  4. Sep 7, 2008 #3


    User Avatar

    Are you trying to find http://en.wikipedia.org/wiki/Compactification_%28mathematics%29" [Broken] of N by adding k points at infinity?

    You can split N into k identical copies, according to their remainders under division by k (modulo k) and add one point at infinity for each of these equivalence classes.
    Last edited by a moderator: May 3, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook