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Spring Topology and Dynamics Conference 2006
March 23-25, 2006
University of North Carolina at Greensboro
Greensboro, NC, USA

Organizers
Gregory Bell, Alexander Chigogidze, Paul Duvall, Jan Rychtar, Jerry Vaughan

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The non-existence of common models for some classes of higher-dimensional hereditarily indecomposable continua
by
Elzbieta Pol
University of Warsaw
Coauthors: Jerzy Krzempek (Silesian University of Technology)

Abstract

A continuum X is a common model for a family K of continua, if every member of K is a continuous image of X. A continuum X is strongly chaotic, if for every two disjoint subsets U and V of X, with U being nonempty and open, there is no homeomorphism from U onto V. We show that none of the following classes of spaces has a common model: 1) the class Kn of strongly chaotic hereditarily indecomposable n-dimensional Cantor manifolds, for any given natural number n, 2) the class K¥ of strongly chaotic hereditarily indecomposable hereditarily strongly infinite-dimensional Cantor manifolds, 3) the class Ka of strongly chaotic hereditarily indecomposable continua with transfinite dimension (small or large) equal to a, for any given countable infinite ordinal number a. Moreover, we show that for any compactification W of the ray and for each of the classes we have described (except for K1), there exists a continuum in this class which can be continuously mapped onto W.

Date received: February 5, 2006

Copyright © 2006 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 # caqs-26.