Continua with unique hyperspace.
by
Gerardo Acosta
Instituto de Matematicas, UNAM. Mexico City

In this talk we define the notion of continuum with unique hyperspace. A continuum X is said to have unique hyperspace if for each continuum Y such that the hyperspaces C(Y) and C(X) are homeomorphic it happens that the continua X and Y are homeomorphic. This notion is a generelization of the notion of familly C-determined introduced by Sam B. Nadler Jr. In this talk we prove that metric compactifications of the space [0, 1) with non-degenerate reminder have unique hyperspace. We prove also that indecomposable continua with all its non degenerate proper subcontinua as arcs have unique hyperspace. This last result is a generalization of a theorem due to Sergio Macías.

Date received: January 15, 1999

Copyright © 1999 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 # caca-09.