How do I prove that two closed intervals,
$\displaystyle [a_1,b_1]=\{x \in \Re : a_1 \le x \le b_1\} \ \& \ [a_2,b_2] \ (a_i <b_i)$ are homeomorphic? Prove by writing down the formula for a homeomorphism.
To prove the homeomorphism you need to find function f:A->B with following properties Homomorphism - Wikipedia, the free encyclopedia.
In your case you have 2 intervals [a1,b1] & [a2,b2]. You can make such function by stretching one interval and then move it to the beginning of the second one.
-------[a1............b1]----------
------------[a2...........b2]------