Group action on \(\mathbb R\times \mathbb Q\) and fine group topologies
type: Item
instance of: scholarly article
title: Group action on \(\mathbb R\times \mathbb Q\) and fine group topologies
zbMATH Open document ID: 1163.54011
published in: Topology and its Applications
publication date: 2009-04-03T00:00:00Z
review text: Under a number of conditions on the base space \(X\), for example T\(_2\) rim-compact and locally connected, the lattice of admissible group topologies on the space \(\mathcal H(X)\) of homeomorphisms, i.e. those topologies for which the evaluation \(\mathcal H(X)\times X\to X\) is continuous, has a least element. A converse, whether non-rim-compact spaces may have this property, is answered by identifying a least element of the lattice of admissible topology on the non-rim-compact space \(\mathbb R\times\mathbb Q\).
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 57S05
Mathematics Subject Classification ID: 54H99
zbMATH DE Number: 5539520
zbMATH Keywords: evaluation function
zbMATH Keywords: admissibility
zbMATH Keywords: Weil uniformity
zbMATH Keywords: uniformity of uniform convergence
zbMATH Keywords: uniform topology
zbMATH Keywords: homeomorphism group
zbMATH Keywords: topological group topologies
zbMATH Keywords: rim-compact spaces
zbMATH Keywords: group action
zbMATH Keywords: fine uniform topology
zbMATH Keywords: fine uniform topology w.r.t. a class of metrics
zbMATH Keywords: fine group topology with respect to a class of metrics
zbMATH Keywords: Whitney topology
zbMATH Keywords: open-cover topology
zbMATH Keywords: limitation topology
author: Anna Di Concilio
MaRDI profile type: Publication
full work available at URL: j.topol.2008.11.013
OpenAlex ID: W2109957996
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DOI: 10.1016/J.TOPOL.2008.11.013
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description: scientific article; zbMATH DE number 5539520