Results 1 to 2 of 2

Math Help - Normal space

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    62

    Normal space

    Is R with lower limit topology normal?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    394
    Quote Originally Posted by math.dj View Post
    Is R with lower limit topology normal?
    \mathbb{Re}_l is regular and Lindelof, so it is normal.

    Let X be \mathbb{Re} with lower limit topology.

    If a \in X and C is a closed subset of X not containing a, then there is a basic open set [a, b) contained in  X\setminus C. Then [a, b) and  X \setminus [a,b) are disjoint open sets containing a and C, respectively. Thus X is regular.

     \mathbb{Re}_l is also Lindelof. It is explained in detail in Munkres p 192.

    However, \mathbb{Re}_l \times \mathbb{Re}_l is neither Lindelof nor normal (see here).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Normal space and Tietze/Urysohn
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: June 11th 2011, 08:33 AM
  2. A normal Moore space is completely normal
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2011, 12:52 PM
  3. [SOLVED] Topology: normal space
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 21st 2010, 11:49 AM
  4. normal topological space
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 5th 2010, 07:07 PM
  5. Normal to a space curve.
    Posted in the Calculus Forum
    Replies: 7
    Last Post: March 17th 2009, 08:30 PM

Search Tags


/mathhelpforum @mathhelpforum