完全不连通集合的超空间

IF 0.5 4区数学 Q3 MATHEMATICS

Glasnik Matematicki Pub Date : 2020-06-12 DOI:10.3336/gm.55.1.10

R. Escobedo, P. Pellicer-Covarrubias, V. Sánchez-Gutiérrez

{"title":"完全不连通集合的超空间","authors":"R. Escobedo, P. Pellicer-Covarrubias, V. Sánchez-Gutiérrez","doi":"10.3336/gm.55.1.10","DOIUrl":null,"url":null,"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.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":"14 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The hyperspace of totally disconnected sets\",\"authors\":\"R. Escobedo, P. Pellicer-Covarrubias, V. Sánchez-Gutiérrez\",\"doi\":\"10.3336/gm.55.1.10\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":55601,\"journal\":{\"name\":\"Glasnik Matematicki\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Glasnik Matematicki\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.55.1.10\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasnik Matematicki","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.55.1.10","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了具有Vietoris拓扑的空间中所有非空闭完全不连通子集的超空间。我们给出了这个超空间的紧性、连通性和局部连通性的结果。我们还研究了路径连通性，特别是证明了对于光滑树状体，该超空间是路径连通的，并给出了一个一般结果，该结果表明对于欧几里德空间，该超空间具有不可数的弧分量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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 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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Glasnik Matematicki MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.