On an example of Simon
type: Item
instance of: scholarly article
title: On an example of Simon
zbMATH Open document ID: 0990.54022
DOI: 10.1016/S0166-8641(01)00065-7
published in: Topology and its Applications
publication date: 2002-05-15T00:00:00Z
review text: The goal of this paper is to provide a method for constructing compactifications \(\alpha\mathbb{N}\) of the positive integers \(\mathbb{N}\) for which the remainder \(\alpha\mathbb{N}-\mathbb{N}\) is sequentially compact and in which no nontrivial sequence of \(\mathbb{N}\) converges. In addition, it is desired that some control be obtained over the other properties of \(\alpha \mathbb{N}-\mathbb{N}\). The authors note Petr Simon previously exhibited such an example in which \(\alpha\mathbb{N} -\mathbb{N}\) is 0-dimensional. In the current paper, the authors' technique is used to provide an example with \(\alpha\mathbb{N} -\mathbb{N}\) connected. Their method is also used to reproduce Simon's example.
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1741959
zbMATH Keywords: sequential compactness
zbMATH Keywords: totally divergent sequences
zbMATH Keywords: compactifications
author: Gary D. Faulkner
author: Maria Cristina Vipera
reviewed by: James Hatzenbuhler
MaRDI profile type: Publication
cites work: Q4107197
cites work: Singular Sets and Remainders
cites work: Q3994309
cites work: Q3994935
cites work: Q3270120
cites work: Q3881546
description: scientific article; zbMATH DE number 1741959