  An expansive, monotone operator is dominating; if it is also idempotent it is
a closure operator. Although they have distinct properties, these two kinds of
discrete operators are also intertwined. Every closure operator is dominating;
every dominating operator embodies a closure. Both can be the basis of
continuous set transformations. Dominating operators that exhibit categorical
pull-back constitute a Galois connection and must be antimatroid closure
operators. Applications involving social networks and learning spaces are
suggested
