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Non-empty, compact, disconnected and limit points

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 Attachment 23327 where *E*0 = [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

Re: Non-empty, compact, disconnected and limit points

Show that each is compact, which will give you the first two points. For totally disconnectedness, show that doesn't contain any interval. Show that for each there is such that .