Results 1 to 4 of 4

Math Help - Topology Proof?

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    9

    Topology Proof?

    How can you prove sets
    1---------
    how can u prove the following sets are are open,
    a. the left half place {z: Re z > 0 };
    b. the open disk D(z0,r) for any z_0 \varepsilon C and r > 0.

    2---------
    a. how can u prove the following set is a closed set:
    _
    D(z0, r)


    MY WORKING SO FAR
    1.. could you please give me a hint on how to start a and b as ive researched but still havent got much of an idea. once i get a little hint then ill try solving and show you my working..

    2a.
    --------
    if D(z0,r) is closed, this implies C\S (the compliment) is open. Therefore, for any z not belonging to the set, there is an e > 0 such that D(z,e) C C\S. This further implies z is not a limit point of S which means that it is a closed set?

    is this correct proof for 2a??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,716
    Thanks
    1642
    Awards
    1
    What are you expected to do to show a set is open?
    I ask because 1b is often used as a basic open set.
    Therefore, you must be using some other definition.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2007
    Posts
    9
    hmm well my definition for an open set is :

    the set S is said to be open if intS = S (int = interior)

    is this what you had in mind??

    how about 2a.. have i done that bit correctly?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,716
    Thanks
    1642
    Awards
    1
    Quote Originally Posted by heyo12 View Post
    my definition for an open set is :
    the set S is said to be open if intS = S (int = interior)
    The statement that z_0  \in {\mathop{\rm int}} (S) means that \left( {\exists r > 0} \right)\left[ {\left\{ {z:\left| {z - z_0 } \right| < r} \right\} \subset S} \right].

    Then for #1a, choose  r = \frac{{{\mathop{\rm Re}\nolimits} (z_0 )}}{2}.

    This is a Post Script.
    For 1b, by definition an open disk is its own interior.
    Last edited by Plato; October 7th 2007 at 04:40 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Understanding Topology Proof
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: July 19th 2011, 07:49 AM
  2. Topology Proof
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: March 12th 2011, 02:43 PM
  3. Topology proof
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 11th 2009, 06:20 PM
  4. Topology Proof
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 26th 2008, 06:58 AM
  5. Help with Proof intro topology
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2007, 06:28 PM

Search Tags


/mathhelpforum @mathhelpforum