The hyperspace of totally disconnected sets
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 t...
| Permalink: | http://skupnikatalog.nsk.hr/Record/nsk.NSK01001098341/Details |
|---|---|
| Matična publikacija: |
Glasnik matematički (Online) 55 (2020), 1 ; str. 113-128 |
| Glavni autori: | Escobedo, Raúl (Author), Pellicer-Covarrubias, Patricia, Sánchez-Gutiérrez, Vicente |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.55.1.10 Hrčak |
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| 035 | |a (HR-ZaNSK)001098341 | ||
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| 041 | 0 | |a eng |b eng | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Escobedo, Raúl |4 aut |9 HR-ZaNSK | |
| 245 | 1 | 4 | |a The hyperspace of totally disconnected sets |h [Elektronička građa] / |c Raúl Escobedo, Patricia Pellicer-Covarrubias, Vicente Sánchez-Gutiérrez. |
| 504 | |a Bibliografske bilješke na kraju teksta. | ||
| 504 | |a Abstract. | ||
| 520 | |a 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. | ||
| 653 | 0 | |a Hiperprostor |a Euklidski prostor |a Kontinuum | |
| 700 | 1 | |a Pellicer-Covarrubias, Patricia |4 aut | |
| 700 | 1 | |a Sánchez-Gutiérrez, Vicente |4 aut |9 HR-ZaNSK | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 55 (2020), 1 ; str. 113-128 |w nsk.(HR-ZaNSK)000659858 | |
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| 856 | 4 | 0 | |u https://doi.org/10.3336/gm.55.1.10 |
| 856 | 4 | 0 | |u https://hrcak.srce.hr/239051 |y Hrčak |
| 856 | 4 | 1 | |y Digitalna.nsk.hr |