Results 1 to 2 of 2

Math Help - Infinite dimensional spaces and other questions.

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    18

    Infinite dimensional spaces and other questions.

    thanks, these are some of my questions :

    1-in our lecture notes i face this statement but i can't understand it :
    " it can happen for infinite dimensional spaces , that 𝐸𝑖⊕ 𝐸𝑖⊥ ≠ E. example :let 𝐸𝑖 ⊂ 𝑙2 consist of vectors having only finitely many non-zero components :
    then 𝐸1⊥={0} but 𝐸1 ≠ 𝑙2"
    2- i understand the definition of closed set is complement of open set so intersection of them should be zero , but in Wikipedia for definition of closed set i found Infinite dimensional spaces and other questions.-ball.pngpicture, that shown a ball , it says that interior of this ball is open set and interior and border is closed set , how it is possible ?

    thanks
    Last edited by ebi120; February 26th 2011 at 01:10 AM. Reason: this pic is not correct
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    The characters you have in your first point in your last post are unintelligible. Could you possibly write them up in LaTeX? The \otimes and \perp commands might be useful.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: January 3rd 2012, 01:56 PM
  2. Infinite Dimensional Banach Spaces
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 23rd 2011, 12:46 PM
  3. Infinite-dimensional vector spaces and their bases!
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: July 23rd 2010, 02:42 PM
  4. Infinite Dimensional Vector Spaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 9th 2009, 09:02 AM
  5. Infinite dimensional Hilbert spaces
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: February 10th 2006, 03:35 PM

Search Tags


/mathhelpforum @mathhelpforum