In this answer, Brian M. Scott lists different definitions of continuity, and for some of them mentions whether they are covariant or contravariant. I am familiar with these terms from subtyping in programming, but I haven't seen these terms applied to mathematical definitions before.
Some questions I have:
- What does it mean for a definition to be covariant or contravariant? Is there a precise definition or is it more informal?
- When can a definition be covariant or contravariant? What are some other examples of covariant or contravariant definitions?
- Is there a way to search for this usage of these terms? When I try to search for the application of these terms to definitions, the search engine (understandably) mistakenly assumes I am looking for the definitions of these terms.