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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 icon 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

Fulltext: english, pdf (182 KB) pages 113-128 downloads: 178* cite
APA 6th Edition
Escobedo, R., Pellicer-Covarrubias, P. & Sánchez-Gutiérrez, V. (2020). The hyperspace of totally disconnected sets. Glasnik matematički, 55 (1), 113-128. https://doi.org/10.3336/gm.55.1.10
MLA 8th Edition
Escobedo, Raúl, et al. "The hyperspace of totally disconnected sets." Glasnik matematički, vol. 55, no. 1, 2020, pp. 113-128. https://doi.org/10.3336/gm.55.1.10. Accessed 18 Oct. 2021.
Chicago 17th Edition
Escobedo, Raúl, Patricia Pellicer-Covarrubias and Vicente Sánchez-Gutiérrez. "The hyperspace of totally disconnected sets." Glasnik matematički 55, no. 1 (2020): 113-128. https://doi.org/10.3336/gm.55.1.10
Harvard
Escobedo, R., Pellicer-Covarrubias, P., and Sánchez-Gutiérrez, V. (2020). 'The hyperspace of totally disconnected sets', Glasnik matematički, 55(1), pp. 113-128. https://doi.org/10.3336/gm.55.1.10
Vancouver
Escobedo R, Pellicer-Covarrubias P, Sánchez-Gutiérrez V. The hyperspace of totally disconnected sets. Glasnik matematički [Internet]. 2020 [cited 2021 October 18];55(1):113-128. https://doi.org/10.3336/gm.55.1.10
IEEE
R. Escobedo, P. Pellicer-Covarrubias and V. Sánchez-Gutiérrez, "The hyperspace of totally disconnected sets", Glasnik matematički, vol.55, no. 1, pp. 113-128, 2020. [Online]. https://doi.org/10.3336/gm.55.1.10

Abstracts
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

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