engleski

Hyperspaces which are products or cones

Let C(X) be the hyperspace of all subcontinua of a metric continuum X. Alejandro Illanes has proved that C(X) is a finite dimensional Cartesian product if and only if X is an arc or a circle. In this paper we shall prove, using the inverse systems and limits, that if X is a non-metric rim-metrizable continuum and C(X) is a finite dimensional Cartesian product, then X is a generalized arc or a generalized circle. It is also proved that if X is a non-metric continuum such that dim(X) < ∞ and such that X has the cone = hyperspace property, then X is a generalized arc, a generalized circle, or an indecomposable continuum such that each nondegenerate proper subcontinuum of X is a generalized arc.

Hyperspace; inverse system

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