Hyperspaces and open monotone maps
of hereditarily indecomposable continua
Abstract: We prove the following theorems:
Theorem 1. Let be an -dimensional hereditarily indecomposable continuum. Then there exist -dimensional hereditarily indecomposable continua and monotone maps such that is an embedding and the space of all subcontinua of is embeddable in by .
Theorem 2. For every open monotone map with non-trivial sufficiently small fibers on a finite dimensional hereditarily indecomposable continuum with there exists a -dimensional subcontinuum such that and the restriction of to is also monotone and open.
The connection between these theorems and other results in Hyperspace theory is studied.
Affiliation: Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel
Address at time of publication: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email: email@example.com, firstname.lastname@example.org
Keywords: Hyperspaces, hereditarily indecomposable continua, open monotone maps
Received by editor(s): January 1, 1995
Communicated by: James West
Article copyright: © Copyright 1997 American Mathematical Society