The surjective reflection between two Cantor Seth [closed]

Let $\mathcal{C}_1$ and $\mathcal{C}_2$ be any two Cantor sets (constructed in Exercise 3.) Show that there exists a function $F:[0,1] \to [0,1]$ with the following properties:

1. $F$ is continuous and bijective,
2. $F$ is monotonically increasing,
3. $F$ maps $\mathcal{C}_{1}$ onto $\mathcal{C}_{2}$

The discribe of exercise 3 is as followed:consider the unit interval [0,1], and let $\xi$ be a real number with $0<\xi<1$In stage 1 of the construction, remove the centrally situated open interval in [0,1] of length $\xi$. In stage 2, remove two central interval s each of relative length $\xi$, one in each of the remaining intervals after stage 1, and so on.

Let $\mathcal{C}_{\xi}$ denotes the set which remains after applying the above procedure indefinitely.