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Math Help - find the closure of A in the co-finite topology

  1. #1
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    find the closure of A in the co-finite topology

    Suppose that X is an infinite set with the co-finite topology, and A \subseteq X. Find Cl(A) in the cases where
    (a) A finite and (b) A infinite.

    I really dont know where to start. Hints would be very useful.

    Thanks
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  2. #2
    Super Member girdav's Avatar
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    Re: find the closure of A in the co-finite topology

    Hint: the closed set are the finite subsets of X and X.
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    Re: find the closure of A in the co-finite topology

    Quote Originally Posted by FGT12 View Post
    Suppose that X is an infinite set with the co-finite topology, and A \subseteq X. Find Cl(A) in the cases where
    (a) A finite and (b) A infinite.
    Question: What is closure of a closed set?
    In part a), is X\setminus A an open set? Why or why not?
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