Electronic Version 16 (1991), 63-87

Alejandro Illanes

Let C(X) be the hyperspace of all subcontinua of a continuum X. In this paper we introduce the concept of semi-boundary. Given A in C(X) - { X }, a subcontinuum B of A is in the semi-boundary of C(A) if there exists a map \alpha: [0,1] --> C(X) such that \alpha(0) = B and \alpha(t) in not contained in A for every t > 0. Using semi-boundaries we obtain characterizations of the interval, simple closed curves, local connectedness, acyclic finite graphs, hereditarily indecomposable continua, atriodic continua and continua containing n-ods.

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topology proceedings Electronic Version