The co-elementary hierarchy is a nested ordinal-indexed sequence of
classes of mappings between compacta, with each successor level being
defined inductively from the previous one using the topological
ultracopower construction.
The lowest level is the class of continuous surjections; and the next
level up, the co-existential maps, is already a much more restricted
class.
Co-existential maps are weakly confluent, and monotone when their images
are locally connected.
These maps also preserve important topological properties, such as:
being infinite, being of covering dimension <= n, and being a
(hereditarily decomposable, indecomposable, hereditarily
indecomposable) continuum.
