We define a Cantor set in the real line as a set that is:
- with empty interior
Is it true that if we have 2 sets in the real line with this properties (and no countable because the singleton also has this) then they are homeomorphic?
Please don't give me a solution, I want to do this problem, but i need some advice. Clearly if I have a continuous bijection then it'll be a homeomorphism.
Because the closed sets are compact and $f$ continuous map preserve this property, and so the image is also closed, so this map is also homeomorphism. But I don't know how to use the property of empty interior in this problem.