Results 1 to 5 of 5

Math Help - Y is a subspace of a X which is a topology

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Y is a subspace of a X which is a topology

    Let Y be a subspace of X. If A is closed in Y and Y is closed in X, then A is closed in X.

    First are there 2 cases to consider? (1) A is a proper subset of Y (2) A=Y\cap U or does this not matter?

    Anyways, all I have is this:

    Since A is closed in Y, Y-A is open in Y. Likewise, X-Y is open in X.

    I am not sure what to do next.
    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

    Re: Y is a subspace of a X which is a topology

    Quote Originally Posted by dwsmith View Post
    Let Y be a subspace of X. If A is closed in Y and Y is closed in X, then A is closed in X.

    First are there 2 cases to consider? (1) A is a proper subset of Y (2) A=Y\cap U or does this not matter?

    Anyways, all I have is this:

    Since A is closed in Y, Y-A is open in Y. Likewise, X-Y is open in X.

    I am not sure what to do next.
    By definition that A is closed in Y you have that A=Y\cap C for some closed subset C of X....so.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Re: Y is a subspace of a X which is a topology

    Quote Originally Posted by Drexel28 View Post
    By definition that A is closed in Y you have that A=Y\cap C for some closed subset C of X....so.
    I don't know. All I can think of is to do Y-(Y\cap A) then but I don't see how that will help.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Re: Y is a subspace of a X which is a topology

    Ok, I think I have it.

    A=Y\cap U where U is some closed set in X. Now, A is the intersection of two closed sets in X so A is closed in X.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: Y is a subspace of a X which is a topology

    Quote Originally Posted by dwsmith View Post
    Ok, I think I have it.

    A=Y\cap U where U is some closed set in X. Now, A is the intersection of two closed sets in X so A is closed in X.
    Correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Subspace Topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 29th 2009, 05:52 PM
  2. Subspace topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 1st 2009, 01:44 AM
  3. The subspace topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 28th 2009, 07:42 PM
  4. Subspace topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 28th 2009, 11:10 AM
  5. subspace topology relationships
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 3rd 2009, 06:44 PM

/mathhelpforum @mathhelpforum