Results 1 to 2 of 2

Math Help - Set Question, deleted neighborhood

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    175

    Set Question, deleted neighborhood

    For this question,

    Prove: for each x in R and  \varepsilon > 0, N^*(x , \varepsilon) is an open set.

    why does it suffice to show that the set is open by showing that every point of the set is an interior point?

    EDIT: sorry if this or any of some of my future questions are trivial, i think this one is, but my professor has been hard to reach these past 2 weeks.
    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 p00ndawg View Post
    For this question,

    Prove: for each x in R and  \varepsilon > 0, N^*(x , \varepsilon) is an open set.

    why does it suffice to show that the set is open by showing that every point of the set is an interior point?

    EDIT: sorry if this or any of some of my future questions are trivial, i think this one is, but my professor has been hard to reach these past 2 weeks.
    An open set is defined to be a set such that all it's points are interior points.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. deleted neighborhood of limit L
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: September 6th 2012, 05:08 PM
  2. Just deleted my working
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 12th 2009, 06:15 AM

Search Tags


/mathhelpforum @mathhelpforum