# What is an interval contiguous to the Cantor set?

I have been reading the answer to Examples of Baire class 2 functions , and I'm trying to see what is an example of an interval contiguous to the Cantor set. Could someone lend me a hand?

• Sounds like it means on the internals that are not part of the Cantor set. – jdods May 26 '18 at 1:02

I imagine that by "interval contiguous to the Cantor set" it means one of the "holes" you cut out when constructing the Cantor set. These are the intervals which are disjoint form the Cantor set but their endpoints are in the Cantor set. So for instance, one such interval is $(1/3,2/3)$: $1/3$ and $2/3$ are in the Cantor set, but nothing in between them is. This is the first third you remove from $[0,1]$ to construct the Cantor set.