Advanced Knowledge Problem of the Week

Here's a new Advanced Knowledge Problem of the Week from the Center of Math! This one's from the field of analysis, and deals with a very peculiar metric space, even though it's built out of some of the most basic ones. 

Think you've figured it out? Find out below...






Did you find another way of showing this result? What other properties can you find about the complement of S_l? Tell us in the comments, and don't forget to look at our other Problems of the Week.