The structure of regular disjoint groups of real homeomorphisms

The structure of disjoint iteration groups of real homeomorphisms has been determined by M. C. Zdun without any regularity condition. In this paper we turn to the regular case and describe the structure of regular disjoint groups of real homeomorphisms which are generalizations of regular disjoint iteration groups. It is shown that such a group is either embedded in a regular iteration group, or it is homeomorphically conjugate to a regular piecewise linear disjoint group.