An anti-Hausdorff Fréchet space in which convergent sequences have unique limits
type: Item
instance of: scholarly article
title: An anti-Hausdorff Fréchet space in which convergent sequences have unique limits
zbMATH Open document ID: 0789.54033
DOI: 10.1016/0166-8641(93)90147-6
author: Eric K. van Douwen
published in: Topology and its Applications
publication date: 1993-11-15T00:00:00Z
review text: The author's introduction: ``We answer an old question of Novák by constructing an anti-Hausdorff Fréchet space in which convergent sequences have unique limits. An essential ingredient in our construction is that there exists an infinite maximal almost disjoint family \({\mathcal A}\) on \(\omega\) and a function \(L:{\mathcal A}\to\omega\) such that for all \(X \subseteq \omega\), if \({\mathcal F}=\{A \in{\mathcal A}:| A \cap X |= \omega \}\) is infinite then \(L^ \to {\mathcal F}=\omega\). We also discuss possible strengthenings and generalizations of this result.
reviewed by: A.I.Bashkirov
Mathematics Subject Classification ID: 54D55
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 446214
zbMATH Keywords: anti-Hausdorff Fréchet space
Wikidata QID: Q56049233
MaRDI profile type: Publication
full work available at URL: 0166-8641(93)90147-6
OpenAlex ID: W2087170117
cites work: Almost-disjoint sets the dense set problem and the partition calculus
cites work: On a property of families of sets
cites work: Some Examples in Topology
cites work: Set theory.
cites work: Happy families
cites work: Q5775624
cites work: Q3918732
description: scientific article; zbMATH DE number 446214