Exercise 1, § 2

A point a ∈ R is said to be left adherent to a subset A of R if it lies in the closure of A and if there is an interval ]a, b[ (a < b) not containing any point of A. Show that the set of left adherent points of a subset A of R is countable (set up a one-to-one correspondence between the set of left adherent points and a set of pairwise disjoint open intervals). Hence show that every well-ordered subset of R is countable.