Results 1 to 4 of 4

Math Help - Topology definition (open/closed)

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Stockholm
    Posts
    5

    Topology definition (open/closed)

    Is the set from -infinity to +infinity open, closed, neither and/or both?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,695
    Thanks
    619

    Re: Topology definition (open/closed)

    Hey Bamsefar.

    This is an interesting question: I guess one way to look at it is if you can construct a complementary set with respect to the real numbers and the complementary set is the empty set.

    So is the empty set open, closed, neither and/or both?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Stockholm
    Posts
    5

    Re: Topology definition (open/closed)

    If I'm not mistaken the empty set is both open and closed by definition, which would mean that the answer to my original question is also "both".
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,708
    Thanks
    1638
    Awards
    1

    Re: Topology definition (open/closed)

    Quote Originally Posted by Bamsefar View Post
    If I'm not mistaken the empty set is both open and closed by definition, which would mean that the answer to my original question is also "both".
    In any topology on a set X both X~\&~\emptyset are both open and closed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exercise with homeomorphism, open and closed: topology
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: June 27th 2011, 08:29 PM
  2. a topology such that closed sets form a topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: June 14th 2011, 04:43 AM
  3. Basic Topology, closed and open sets
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 3rd 2010, 11:43 PM
  4. Open and Closed set topology question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 17th 2009, 12:42 PM
  5. Topology Open/Closed Sets
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 27th 2008, 06:52 PM

Search Tags


/mathhelpforum @mathhelpforum