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Mathematical Communications, Vol. 6 No. 2, 2001.

Original scientific paper

Hyperspaces which are products or cones

I. Lončar

Full text: english pdf 223 Kb

page 199-215

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Abstract

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 ageneralized arc, a generalized circle, or an indecomposable continuum such that each nondegenerate proper subcontinuum of X is a generalized arc.

Keywords

hyperspace; inverse system

Hrčak ID:

827

URI

https://hrcak.srce.hr/827

Publication date:

20.12.2001.

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