Examples from trees, related to discrete subsets, pseudo-radiality and \(\omega \)-boundedness
type: Item
instance of: scholarly article
title: Examples from trees, related to discrete subsets, pseudo-radiality and \(\omega \)-boundedness
zbMATH Open document ID: 1162.54017
author: Leandro F. Aurichi
published in: Topology and its Applications
publication date: 2009-03-06T00:00:00Z
review text: Discrete subspaces have been shown to be subspaces that can say much about the whole space. For example, discretely reflexive properties and discretely generated properties have been discussed in the past few years. In this paper the author presents some constructions using trees, mainly Souslin trees, that give counterexamples for the discrete reflection of certain topological properties. Also, assuming the existence of a Souslin tree, a compact space that is pseudo-radial but not discretely generated is constructed. A first-countable space that is \(\omega\)-bounded but not strongly \(\omega\)-bounded is given using an Aronszajn tree.
Mathematics Subject Classification ID: 54G20
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54D99
Mathematics Subject Classification ID: 03E65
zbMATH DE Number: 5526275
zbMATH Keywords: Souslin trees
zbMATH Keywords: Aronszajn trees
zbMATH Keywords: discrete reflection
zbMATH Keywords: \(\omega\)-bounded
zbMATH Keywords: discretely generated
zbMATH Keywords: radial spaces
reviewed by: Shou Lin
MaRDI profile type: Publication
full work available at URL: j.topol.2008.09.015
OpenAlex ID: W2037436541
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DOI: 10.1016/J.TOPOL.2008.09.015
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description: scientific article; zbMATH DE number 5526275