Showing path connected

  • Thread starter muzak
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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.
 

Answers and Replies

  • #2
Dick
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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.
 

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