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Math Help - Is it the discreate topology

  1. #1
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    Is it the discreate topology

    Consider the Natural numbers N. and t the collection of all subsets G which satisfy the condition: if {n\in\mathbb{G}} and m|n, then {m\in\mathbb{G}}. Show that t is a topology on N. Is it the discrete topology.

    I can show all the conditions for t eccept that {N\in\mathbb} t and {(the empty set)\in\mathbb} t


    Is it the discrete topology?? I have no idea about this.

    help please
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  2. #2
    Super Member girdav's Avatar
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    Re: Is it the discreate topology

    For G=\emptyset, the statement n\in G is always false and it implies everything, in particular m\in G if m\mid n. If n\in \mathbb N and m\mid n, then m should be an integer.
    Hint for the question: if n=p_1p_2 where p_1 and p_2 are prime numbers then a set of the topology which contains n should contain p_1 and p_2.
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