Results 1 to 3 of 3

Math Help - question about general topological spaces

  1. #1
    Member
    Joined
    Apr 2008
    From
    Seoul, South Korea
    Posts
    128

    question about general topological spaces

    X is a set and T be the family of subsets U of X such that X\U is finite, together with the empty set. show that T, the cofinite topology of X, is a topology. i think that it is obvious that condition 1 holds, but i am finding it difficult to show condition 2 and 3 (any union of sets in T belongs to T and that any intersection of sets in T belong to T). thanks in advance for help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2008
    From
    Seoul, South Korea
    Posts
    128
    actually i just saw that to show the union part is pretty trivial. but i cannot seem to figure out the intersection part.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1
    BTW: The third condition says finite intersection.
    If each of O & Q is cofinite then \left( {O \cap Q} \right)^c  = O^c  \cup Q^c . The union of two finite sets is a finite set.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Topological Spaces
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 19th 2010, 09:14 PM
  2. Topological Spaces
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 4th 2010, 10:01 AM
  3. about topological spaces
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: June 30th 2009, 04:28 AM
  4. Hoeomorphic topological spaces
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2009, 04:55 PM
  5. question about topological spaces
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 19th 2008, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum