Results 1 to 2 of 2

Math Help - finite complement topology

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    1

    finite complement topology

    What are the closed sets in a finite space with the finite complement topology?

    What are the closed sets in a infinite space with the finite complement topology?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by bkzyankeechic View Post
    What are the closed sets in a finite space with the finite complement topology?
    Come on:

    Spoiler:


    If X is finite then given any E\subseteq X we have that X-E\subseteq X is finite and thus E is open. Thus, X is discrete...sooo.



    What are the closed sets in a infinite space with the finite complement topology
    Come on (with equal exasperation):

    Spoiler:


    If X is infinite and E\subseteq X is closed then E=X-O for some open O\subseteq X but by definition this means that E is finite

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the closure of A in the co-finite topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 13th 2011, 11:55 AM
  2. [SOLVED] Finite Compliment Topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 9th 2011, 11:46 AM
  3. Topology, complements of finite sets
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 4th 2010, 08:32 AM
  4. finite compliment and discrete topology question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 17th 2009, 12:54 PM
  5. how to show dense in Finite complement topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 16th 2009, 10:35 AM

Search Tags


/mathhelpforum @mathhelpforum