The most important notion in this book are "funcoids".
Then in the chapter 14 I consider "pointfree funcoids", a trivial generalization of funcoids. I do exactly this thing (trivial generalization) about many theorems about funcoids transforming them into theorems about pointfree funcoids.
In this book I also do similar thing with generalization "filters on sets" -> "filters on posets" -> "filtrators".
In every of these generalizations I leave unchanged the same the conclusion of the theorem, changing only the conditions.
Having said all that, I slightly feel that I haven't presented it in the best possible way.
I want to hear some comments on this, not sure what exactly the nature of comments I want to hear.