Congruences on semigroups of continuous selfmaps (Q801165)

Let S(X) be the semigroup of all continuous selfmaps of a topological space X. The author considers a certain type of functions whose domain is a nonempty collection of subsets of X and whose range is a collection of subsets of S(X), and with each such function he associates a congruence on S(X). Then he investigates in more detail certain natural subclasses of this rather general class of congruences, especially their order- and lattice-theoretic properties. The results obtained are applied to special Peano continua (the so called B-dendrites).