REGULAR MINIMAL SETS, I.

A central problem in topological dynamics is the classification of minimal sets. In full generality, this problem appears to be quite difficult. Therefore, it seems appropriate to single out certain minimal sets which are well behaved in some sense, and therefore more amenable to classification. It is for this purpose that we introduce the regular minimal sets in this paper. They are the universal minimal sets for certain admissible properties. Several characterizations are given theorem 3 the class of regular minimal sets is shown to coincide with the minimal right ideals of enveloping semigroups of transformation groups. and also with those minimal sets having a maximal supply of endomorphisms. Author