Commuting self-maps of the simple triod
by
Eric McDowell
Berry College

Let T denote the simple triod. The question of whether there exist continuous functions f, g:T→ T for which fg=gf and f(x) ≠ g(x) for some x ∈ T was probably asked in the 1970s or 1980s; however, the original author of the question is unknown. A positive answer to this question would allow the construction of a (simple triod)-like continuum admitting a fixed point free map, while a negative answer would generalize the fixed point property of the simple triod. We provide a negative answer to this question in the case when f and g are monotone mappings.

Date received: February 26, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawk-80.