Results 1 to 1 of 1

Math Help - Initial topology

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    /
    Posts
    7

    Initial topology

    Hi,

    In my course topology there's a propisition which says the following: suppose f and g are continuous functions and f \circ g is initial then g is initial (I mean with initial that f \circ g and g have the initial topology on their domains).

    Now, they ask for a counterexample. I have to give an example where g and f \circ g are initial but g is not a continuous function.

    The problem is that I don't have an idea how to construct an initial function.

    Anyone?
    Last edited by Impo; January 8th 2013 at 10:53 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Topology proof: smallest topology and base for topology
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: October 18th 2012, 02:49 PM
  2. Problem on product topology/standard topology on R^2.
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: October 17th 2012, 01:22 AM
  3. Topology: product, uniform, and box topology converging sequences
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 2nd 2012, 04:58 PM
  4. a topology such that closed sets form a topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: June 14th 2011, 05:43 AM
  5. Show quotient topology on [0,1] = usual topology on [0,1]
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 5th 2010, 05:44 PM

Search Tags


/mathhelpforum @mathhelpforum