Original scientific paper

https://doi.org/10.3336/gm.44.2.12

Compactifications of [0,∞) with unique hyperspace Fn(X)

Alejandro Illanes ; Universidad Nacional Autónoma de México, Instituto de Matemáticas, Circuito Exterior, Cd. Universitaria, México, 04510, D.F. Mexico
Jorge M. Martinez-Montejano ; Universidad Nacional Autónoma de México, Instituto de Matemáticas, Circuito Exterior, Cd. Universitaria, México, 04510, D.F. Mexico

Abstract

Given a metric continuum X, Fn(X) denotes the hyperspace of nonempty subsets of X with at most n elements. In this paper we show the following result. Suppose that X is a metric compactification of [0,∞), Y is a continuum and Fn(X) is homemorphic to Fn(Y). Then: (a) if n ≠ 3, then X is homeomorphic to Y, (b) if n = 3 and the remainder of X is an ANR, then X is homeomorphic to Y. The question if the result in (a) is valid for n = 3 remains open.

Keywords

Compactification; continuum; hyperspace; ray; symmetric product; unique hyperspace

Hrčak ID:

44056

URI

https://hrcak.srce.hr/44056

Publication date:

9.12.2009.

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