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Math Help - how many topologies can be made

  1. #1
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    how many topologies can be made

    How many topologies can be made with
    a set that has 2 points, and a set that has 3 points, and a set that has 4 points??

    My guess for the 2 points are if A = {a,b}
    topology of A can be {emptyset, {a,b}} or {emptyset, {a}, {b}}.

    but can the set {emptyset, {a}} be a topology of A? thank you
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  2. #2
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    Quote Originally Posted by pandakrap View Post
    How many topologies can be made with
    a set that has 2 points, and a set that has 3 points, and a set that has 4 points??
    My guess for the 2 points are if A = {a,b}
    topology of A can be {emptyset, {a,b}} or {emptyset, {a}, {b}}.
    but can the set {emptyset, {a}} be a topology of A? thank you
    Read carefully the requirments for a topology.
    Now look at what you wrote.
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