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Math Help - topology?

  1. #1
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    topology?

    Given a set X={a,b,c} is the following subset a topology for X:
    { X,{a},{b},{a,b},{a,c},{empty set} } ?
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  2. #2
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    Quote Originally Posted by bigdoggy View Post
    Given a set X={a,b,c} is the following subset a topology for X:
    { X,{a},{b},{a,b},{a,c},{empty set} } ?
    Does it satisfy the criteria for a topology?
    1) Does it include the empty set?
    Yes.
    2) Does it include X itself?
    Yes.
    3) If it includes set U and V does it include U\cap V.
    Since there are only 6 sets here, you could just check every possible intersection- yes, it does,.
    4) Are all possible unions of members of the collection in the collection?
    Again, there are only a finite number of unions to try- yes, it does.

    So this is, in fact, a topology for X.
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