Original scientific paper

https://doi.org/10.3336/gm.55.1.10

The hyperspace of totally disconnected sets

Raúl Escobedo ; Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 sur, Col. San Manuel, Edificio FM3-210, Ciudad Universitaria C.P. 72570, Puebla, México
Patricia Pellicer-Covarrubias ; Departmento de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, Ciudad de México, C.P. 04510, México
Vicente Sánchez-Gutiérrez orcid.org/0000-0002-9247-9375 ; Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 sur, Col. San Manuel, Edificio FM3-210, Ciudad Universitaria C.P. 72570, Puebla, México

Abstract

In this paper we study the hyperspace of all nonempty closed totally disconnected subsets of a space, equipped with the Vietoris topology. We show results of compactness, connectedness and local connectedness for this hyperspace. We also include a study of path connectedness, particularly we prove that for a smooth dendroid this hyperspace is pathwise connected, and we present a general result which implies that for an Euclidean space this hyperspace has uncountably many arc components.

Keywords

Continuum, hyperspace; locally connected; pathwise connected; totally disconnected set

Hrčak ID:

239051

URI

https://hrcak.srce.hr/239051

Publication date:

12.6.2020.

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