I am at the moment trying to get through some basic set theory and I'm getting very stuck with the proofs. This question is from a textbook I am studying from and as it is a prove question there is no solution in the back
Any help with explanations would be very useful
Let where E0 = [0, 1] and Ek is constructed by removing the
second, fourth and sixth sevenths of each component Ek-1. Each set that is removed is open.
I need to show that F is non-empy, compact, totally disconnected and that 0 is a limit point of F