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Math Help - Open and Closed set topology question

  1. #1
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    Open and Closed set topology question

    Let be a collection of subset of the set X, satisfying:

    i. and X contained in ,
    ii. finite unions of elements in are in , and
    iii. arbitrary unions of elements in are in

    We know that is a topology on X

    Give an example of a topology when X = . What are the open sets in this topology?What are the closed sets? What is the basis for the topology?
    Last edited by mr fantastic; May 22nd 2009 at 04:10 AM. Reason: Restored question deleted by OP
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  2. #2
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    Quote Originally Posted by flaming View Post
    Let be a collection of subset of the set X, satisfying:

    i. and X contained in ,
    ii. finite unions of elements in are in , and
    iii. arbitrary unions (intersections?) of elements in are in

    We know that is a topology on X
    I assume you mean arbitrary intersections because both "finite unions" and "arbitrary unions" conditions at the same time do not make much sense.

    Give an example of a topology when X = .
    Cofinite topology on R

    What are the open sets in this topology?What are the closed sets?
    Finite point sets are closed in the cofinite topology on \mathbb{R}.

    What is the basis for the topology?
    A subbasis of a cofinite topology on R is the set of complements of singletons in R. You can get the basis for a cofinite topology on R using the subbasis.
    Last edited by aliceinwonderland; April 17th 2009 at 03:52 PM.
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