Hyperspaces and cones
by
Piotr Minc
Auburn

It was proved by H. Bell (1967), K. Sieklucki (1968) and S. Iliadis (1970) that if f is a mapping of a nonseparating plane continuum X into itself, then there is an indecomposable subcontinuum W of X such that f(W) subset W. (A continuum is indecomposable if it is not the union of its two proper subcontinua.) In 1976, R. Ma\'nka proved that every tree-like continuum without the fixed point property must contain an indecomposable continuum. (A continuum is tree-like if it is the inverse limit of a sequence of trees.) In 1978, D.P. Bellamy gave his classic example of a tree-like continuum without the fixed point property. Subsequently (in 1983) Bellamy asked whether every self map of a tree-like continuum must map an indecomposable continuum into itself. It turns out that Bellamy's construction can be modified to answer his question by a counterexample.

Date received: February 18, 1997

Copyright © 1997 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 # caak-45.