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Homework Help: Showing path connected

  1. Sep 23, 2012 #1
    1. The problem statement, all variables and given/known data
    I am given a set S consisting of the union of line segments from the point (0,1) to points (x,0) x-values are rationals from [0,1]. I want to show that this is path connected.

    2. Relevant equations
    Finding a continuous function f:[0,1] -> S such that f(0) = a and f(1) = b where a,b are in the set.

    3. The attempt at a solution

    I don't know how to show this part, do I attempt to show continuity in the topological sense? I don't even know how to attempt that. I'm having a hard time conceptualizing continuity with this.
  2. jcsd
  3. Sep 23, 2012 #2


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    Science Advisor
    Homework Helper

    You've got a bunch of line segments that are all connected to (0,1). Just go from a to (0,1) and then from there to b.
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