We adopt throughout the convention that compact spaces are Hausdorff.
We adopt the convention that the first coordinate $i$ increases as one goes downwards, and the second coordinate $j$ increases as one goes from left to right.
To avoid undue repetition in the statements of our theorems, we adopt the following convention.
This is the point of view adopted in Section 3.
Furthermore, adopting this strategy considerably eases constructing a coding tree from a linear order.
We could have adopted an approach to proving Theorem 2 along a line of reasoning which bears greater resemblance to the treatment of the analogous result in Section 1.