Page "Domain theory" Paragraph 13

Now that we have some basic formal descriptions of what a domain of computation should be, we can turn to the computations themselves.

Clearly, these have to be functions, taking inputs from some computational domain and returning outputs in some ( possibly different ) domain.

However, one would also expect that the output of a function will contain more information when the information content of the input is increased.

Formally, this means that we want a function to be monotonic.