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Inverse Limits with u.s.c. Bonding Functions and Indecomposable Continua
by
Scott Varagona
Auburn University
It was shown by Ingram and Mahavier that if f: [0, 1] → 2[0, 1] is an upper semi-continuous bonding function and f(x) is connected for each x ∈ [0, 1], then the inverse limit space with the single bonding function f is a continuum. We present some conditions on the graph of f that are sufficient conditions for the inverse limit space to be a decomposable continuum. We also describe a class of u.s.c. functions whose corresponding inverse limit spaces are indecomposable continua. Finally, we show that a "two-sided" inverse limit with u.s.c. bonding functions may generate a different continuum than the mere "one-sided" one does.
Date received: February 2, 2009
Copyright © 2009 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 # caxy-33.