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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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Continua X with a small-point hyperspace homeomorphic to X×[0, 1]
by
Eric L. McDowell
Berry College
Coauthors: W.J. Charatonik

Let X be a metric continuum. If d is a metric on X and e > 0, we define the small-point hyperspace of X with respect to d and e to be all those members of C(X) with d-diameter ≤ e. Some continua X have a small-point hyperspace that is homeomorphic to X×[0, 1]; we refer to such spaces as C-H(e) continua. In this talk, we will show that the eight hereditarily decomposable continua for which C(X) is homeomorphic to Cone(X) are also C-H(e) continua. Moreover, we will demonstrate that many more such C-H(e) continua exist.

Date received: March 1, 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 # cast-36.