A note on topological properties of non-Hausdorff manifolds
type: Item
instance of: scholarly article
title: A note on topological properties of non-Hausdorff manifolds
zbMATH Open document ID: 1182.54059
DOI: 10.1155/2009/891785
author: Steven L. Kent
author: Roy A. Mimna
author: Jamal K. Tartir
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45739
review text: In this short note, the authors introduce the notion of compatible apparition points for a non-Hausdorff manifold. Let \(M\) be a non-Hausdorff manifold and let \(x\), \(y\) be distinct points of \(M\). Then \(x\) and \(y\) are compatible apparition points if there do not exist disjoint open sets \(U\) and \(V\) with \(x \in U\) and \(y \in V\). A set of compatible apparition points is a set such that any pair of distinct points in that set are compatible apparition points. The authors prove some elementary properties of such sets. They show that a set of compatible apparition points in a non-Hausdorff manifold \(M\) is nowhere dense in \(M\). They also show that if \(M\) contains a non-empty set \(S\) of compatible apparition points, then every continuous function from \(M\) to a Hausdorff space \(X\) is constant on \(S\).
reviewed by: Mahender Singh
Mathematics Subject Classification ID: 54H99
Mathematics Subject Classification ID: 57N99
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 5627905
zbMATH Keywords: compatible apparition points
zbMATH Keywords: metacompact space
zbMATH Keywords: non-Hausdorff manifolds
MaRDI profile type: Publication
OpenAlex ID: W2021020994
Wikidata QID: Q58648520
cites work: Homogeneous and inhomogeneous manifolds
cites work: Q4820394
cites work: Manifolds: Hausdorffness versus homogeneity
description: scientific article; zbMATH DE number 5627905