Properness of foliations
type: Item
instance of: scholarly article
title: Properness of foliations
zbMATH Open document ID: 1407.57021
author: Tomoo Yokoyama
published in: Topology and its Applications
publication date: 2019-01-23T00:00:00Z
review text: It is shown that a continuous foliation \(\mathcal F\) on a metrisable manifold \(M\) is proper if and only if the leaf space \(M/\mathcal F\) is \(T_0\). An example of \textit{M. Kneser} [Arch. Math. 11, 280--281 (1960; Zbl 0102.38601)], is recalled of a single leaf codimension one foliation on a non-metrisable 3-manifold that shows that the hypothesis of metrisability is required. A related result for orbits of a continuous flow on a metrisable manifold is presented.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 37B35
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 7005613
zbMATH Keywords: foliations
zbMATH Keywords: proper leaves
zbMATH Keywords: orbit class spaces
zbMATH Keywords: recurrence
MaRDI profile type: Publication
full work available at URL: j.topol.2018.12.008
OpenAlex ID: W2910507701
cites work: Topological Properties of the Solutions of Ordinary Differential Equations
cites work: Foliations with all leaves compact
cites work: Periodic flows on three-manifolds
cites work: Leaves Without Holonomy
cites work: A counterexample to the periodic orbit conjecture in codimension 3
cites work: A counterexample to the periodic orbit conjecture
cites work: Foliations of codimension 2 with all leaves compact
cites work: A periodic flow with infinite Epstein hierarchy
cites work: Foliations with few non-compact leaves
DOI: 10.1016/J.TOPOL.2018.12.008
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description: scientific article; zbMATH DE number 7005613