On uniform connectedness
type: Item
instance of: scholarly article
title: On uniform connectedness
zbMATH Open document ID: 0674.54017
DOI: 10.1155/S0161171289000530
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46383
review text: Summary: The concept of uniform connectedness, which generalizes the concept of well-chainedness for metric spaces, is used to prove the following: (a) If two points a and b of a compact Hausdorff uniform space (X,\({\mathcal U})\) can be joined by a U-chain for every \(U\in {\mathcal U}\), then they lie together in the same component of X; (b) Let (X,\({\mathcal U})\) be a compact Hausdorff uniform space, A and B non-empty disjoint closed subsets of X such that no component of X intersects both A and B. Then there exists a separation \(X=X_ A\cup X_ B\), where \(X_ A\) and \(X_ B\) are disjoint compact sets containing A and B respectively. These generalize the corresponding results for metric spaces.
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54D05
zbMATH DE Number: 4103954
zbMATH Keywords: well-chained metric spaces
zbMATH Keywords: uniformly connected spaces
zbMATH Keywords: compact Hausdorff uniform space
author: Dharmanand Baboolal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4103954