Results 1 to 2 of 2

Math Help - countable connected Hausdorff space

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    49

    countable connected Hausdorff space

    Can anybody tell me what is a countable connected Hausdorff space??

    I know that

    Connected: A topological space is connected if it is not the union of a pair of disjoint sets
    Countable: A set is countable if it is finite or countably infinite
    Hausdorff space: has distinct points which have disjoint neighborhoods.

    So by applying these three definitions does that mean a countable connected Hausdorff space is a finite connected space with disjoint neighborhoods?
    How would one picture this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Turloughmack View Post
    Can anybody tell me what is a countable connected Hausdorff space??

    I know that

    Connected: A topological space is connected if it is not the union of a pair of disjoint sets
    Countable: A set is countable if it is finite or countably infinite
    Hausdorff space: has distinct points which have disjoint neighborhoods.

    So by applying these three definitions does that mean a countable connected Hausdorff space is a finite connected space with disjoint neighborhoods?
    How would one picture this?

    Anyone learning topology should already know that not everything in maths is easy, or even possible, to "picture" in a standard way.

    A countable connected Hausdorf space is a (topological) space which is Hausdorrf, connected and countable...what else do

    you need?! A photo? I don't think there is one, although perhaps there exist somewhere some more "intuitive" descripition of this.

    Perhaps in the book "Counterexamples in Topology", by Steen and Seebach, there's something...

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] A subspace of a Hausdorff space is Hausdorff
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: September 24th 2011, 01:40 PM
  2. Every path-connected metric space is connected
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 13th 2011, 06:31 AM
  3. Connected Hausdorff Spaces
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 18th 2010, 05:20 AM
  4. Connected Hausdorff spaces and graphs
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: March 12th 2010, 10:51 AM
  5. Quotient map from Hausdorff to non-Hausdorff space
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 28th 2009, 05:51 PM

Search Tags


/mathhelpforum @mathhelpforum