All about continua with unique hyperspaces
by
Alejandro Illanes
Universidad Nacional Autónoma de México

Let X be a metric continuum. The hyperspaces of X are: 2X = the space of all nonempty closed subsets of X, C(X) = the space of all subcontinua of X and Fn(X) = the space of all nonempty subsets of X with at most n elements. The continuum X is said to have unique hyperspace C(X) provided that if Y is a continuum and C(X) is homeomorphic of C(Y), then X is homeomorphic to Y. Similar definitions are given for 2X and Fn(X). In this talk we present what is known about uniqueness of hyperspaces, the new results and the open problems.

Date received: February 6, 2002