Proving Path Connectivity of Set S with Rational Line Segments

[muzak]

Homework Statement

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.

Homework 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.

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.

 

[Dick]

Homework Statement

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.

Homework 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.

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.

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.