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 ):

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This formula is equivalent (exercise!) to

.

It can be abstracted/simplified further:

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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).

In my book I have shown that for co-complete funcoids being an “open” is a special case of being continuous (but being continuous this times is defined with the reversed order).