Omega-limit sets in hereditarily locally connected continua
type: Item
instance of: scholarly article
title: Omega-limit sets in hereditarily locally connected continua
zbMATH Open document ID: 1184.37012
author: Vladimír Špitalský
published in: Topology and its Applications
publication date: 2008-06-19T00:00:00Z
review text: This paper gives a topological characterization of \(\omega\)-limit sets in hereditarily locally connected continua \(X\). For a non-degenerate completely regular continuum \(X\) this reduces to the following: a subset of \(X\) is an \(\omega\)-limit set if and only if it is either a finite union of disjoint non-degenerate subcontinua of \(X\) or a nowhere dense closed subset of \(X\). Orbit-enclosing \(\omega\)-limit sets in such \(X\) are also characterized.
reviewed by: Boris Kruglikov
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 5290933
zbMATH Keywords: omega-limit set
zbMATH Keywords: continuum
zbMATH Keywords: hereditarily locally connected continuum
MaRDI profile type: Publication
full work available at URL: j.topol.2008.03.005
OpenAlex ID: W2144305026
cites work: The structure of \(\omega\)-limit sets for continuous functions
cites work: The structure of $\omega$-limit sets for continuous maps of the interval
cites work: Q3024409
cites work: Omega limit sets and distributional chaos on graphs
cites work: Q5436538
cites work: Q5837858
cites work: Q3304890
cites work: Q4004123
cites work: Each Peano subspace of \(E^ k\) is an \(\omega\)-limit set
cites work: What sets can be \(\omega\)-limit sets in \(E^ n\)?
cites work: Q4822100
cites work: On \(\omega\)-limit sets of triangular maps
cites work: On a conjecture of Agronsky and Ceder concerning orbit-enclosing \(\omega \)-limit sets
cites work: Two counterexamples to a conjecture by Agronsky and Ceder
cites work: \(\omega\)-Limit sets for triangular mappings
cites work: Description of \(\omega\)-limit sets of a triangular map on \(I^2\)
cites work: A triangular map on \(I^2\) whose \(\omega\)-limit sets are all compact intervals of \(\{ 0\}\times I\).
cites work: On the structure of transitive \(\omega\)-limit sets for continuous maps
cites work: On \(\omega\)-limit sets of antitriangular maps.
cites work: Q3376449
cites work: Q4278308
cites work: A ``universal'' dynamical system generated by a continuous map of the interval
cites work: The space of $\omega $-limit sets of a continuous map of the interval
cites work: Spaces of ω-limit sets of graph maps
cites work: Hausdorff compactness on a space of \(\omega\)-limit sets
cites work: Minimal Sets on Graphs and Dendrites
cites work: Continua which admit only the identity mapping onto non-degenerate subcontinua
cites work: Dynamics in one dimension
cites work: Q3994935
cites work: Fixed point sets of 1-dimensional Peano continua
cites work: Partitioning continuous curves
cites work: Q5509701
DOI: 10.1016/J.TOPOL.2008.03.005
description: scientific article; zbMATH DE number 5290933