Ueber topologisch homogene Kontinua

A characterization of solenoids

“…If it is 1,1, after some place, the solenoid is a simple closed curve. If it is 2, 2, , the solenoid is the dyadic solenoid defined by D. van Dantzig [7] and L. Vietoris [23]. Other properties involving the sequence n u n 2 , are given in [4, p.…”

Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

“…Indeed, in [15,1], it is shown that two solenoids S P and S P are homeomorphic iff, after perhaps removing a finite number of terms, P and P contain each prime the same number of times. In general, however, non-homeomorphic solenoids may exhibit the same entropies as exemplified by the pair S (2,3,5,7,...) and S (2,2,3,3,5,5,7,7,...) -both solenoids admit only self-homeomorphisms of zero entropy.…”

“…A solenoid goes back to [20,5] and is an indecomposable continuum that can be visualized as intersection of a nested sequence of progressively thinner solid tori that are each wrapped into the previous one a number of times as suggested by Figure 1.1. Any radial cross section of a solenoid is a Cantor set each point of which belongs to a densely immersed line, called a composant.…”

Monothetic algebraic groups

“…For the class of locally compact groups these groups are called monothetic and were introduced by van Dantzig in [14]. The full classification of their structure can be found in [4,Section 25].…”