Hereditarily Indecomposable Continua Have Unique Hyperspace 2^X
by
Sergio Macías
Universidad Nacional Autónoma de México

A continuum is a nonempty, compact, connected, metric space. A subcontinuum of a continuum X is a continuum contained in X. A continuum X is said to be decomposable provided that X=A\cupB, where A and B are proper subcontinua of X. X is indecomposable if it is not decomposable. A continuum is hereditarily indecomposable if each subcontinuum of it is indecomposable. Given a continuum X we define its hyperspace of compact subsets of X by

2X={A subset X | A is a closed and nonempty}

It is known that 2^X is a metric space with the Hausdorff metric. We prove that if X is a hereditarily indecomposable continuum and Y is a continuum such that 2^X is homeomorphic to 2^Y then X is homeomorphic to Y.

Date received: February 12, 1998

Copyright © 1998 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 # caas-67.