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Topology on N 
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#1
Sep408, 10:43 PM

P: 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
Sep508, 02:11 AM

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P: 2,020

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 freestanding topological space, or are you trying to topologize R, and then give N the subspace topology? 


#3
Sep708, 08:14 PM

P: 532

Are you trying to find compactifications 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. 


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