We study Cantor sets which occur as minimal sets for homeomorphisms of R^n. The minimality is modelled on an infinite product of finite cyclic groups and on a generalized adding machine. An interesting example is a homeomorphisms on R^3 which has Antoine’s Necklace as a minimal set. We also discuss some open problems concerning homeomorphism that have a Cantor set as a minimal set (Refer to PDF file for exact formulas).
Department, Program, or Center
School of Mathematical Sciences (COS)
Basener, William, "Exceptional sets and Antoine's necklace" (2007). Accessed from
RIT – Main Campus