In the appendix, I omitted to include the definition of `function´ in section A.4 *Constructive concepts and axioms used*. The reason is that we use the standard classical definition:

Having taken the notion of `set´ and `subset´ as primitive, we define a function from an apartness space to another apartness space as a subset of the cartesian product such that:

i) for all there is a such that

ii) for all : if and and then .

Then for any pair we write: or .

The constructive interpretation of the quantifiers `for all´ and `there is´ ensures in our eyes that this definition nicely captures the connotation of methodicity which the word `function´ carries. In the book we almost always work with morphisms anyway, but the definition above is strictly speaking necessary to underpin the theorems on representability of continuous functions by morphisms.