......, where each function $g$ is as specified above.
Choose a sequence of compact sets $K_n$ with the properties specified in Lemma 3.
The parent and child relations often used with trees can be derived once a root is specified.
In the latter case we may simply adjust $F$ to equal 1 on the Borel set where it falls outside the specified interval.
We take advantage of this fact on several occasions, by not actually specifying the topology under consideration.
We will not normally specify the index set $I$.