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Hi I've got a problem on topology.

Let $\mathcal T$ be the class of subsets of positive integers consisting null set and all subsets of positive integers of the form $E_n =\{n,n+1,n+2,n+3,\dots\}$ with $n$ element of positive integers.

  1. Show that $\mathcal T$ is a topology on the set of positive integers.
  2. List the open sets containing the positive integer $G$.

Could you please help me?

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    What have you tried? Have you tried verifying that this collection satisfies the axioms of a topology?2012-08-03
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    So our sets are $E_n = \{x \geq n:x\in \mathbb{N}^+ \}$. What is the union of $E_n$ and $E_m$ when $n? What about the intersection?2012-08-03
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    Since you are new to this site, you could maybe read this: [How to ask a homework question.](http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question) I wrote this comment because the question sounds homework-like.2012-08-03

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