Let and are endofuncoids and is a funcoid from to .
Then we can generalize Bourbaki’s notion of open mapping between topological spaces (that is a mapping for which images of open sets are open) by the following formula (where is a variable which ranges through entire ):
This formula is equivalent (exercise!) to
It can be abstracted/simplified further:
The last formula looks deceitfully similar to a formula expressing continuous funcoid, but it is unrelated.
That is what open maps are in a higher abstraction level. These seem to posses no interesting properties at all (but I may mistake about this).