"embedded" does not imply that it is still a subset of the line. It just says that it's one-to-one and a homeomorphism with the image. The conjecture requires to prove that there exists a Cantor which cannot be separated from itself, so showing an example where it can be separated is not relevant.

## M

"embedded" does not imply that it is still a subset of the line. It just says that it's one-to-one and a homeomorphism with the image. The conjecture requires to prove that there exists a Cantor which cannot be separated from itself, so showing an example where it can be separated is not relevant.