Cantor set

My first “favorite space” post here is on the Cantor set, and I wrote it because I wanted to write about a function that is based on the Cantor set, and I felt like I was trying to cram way too much into one article.

It feels like everywhere I turn, I run into the Cantor set.

I feel a little weird saying the Cantor set, though, because for the space I’m writing about today, it makes more sense to call it a Cantor set.

Any space with these properties can be called a Cantor set, and in some sense, there's nothing special about the middle-thirds construction.

Sometimes it seems like in the world of interesting mathematical examples, all roads lead to the Cantor set.