The only finite graph that is an inverse limit with a set valued function on \([0,1]\) is an arc
From MaRDI portal
Publication:409508
DOI10.1016/J.TOPOL.2011.11.029zbMath1242.54004OpenAlexW2080686990MaRDI QIDQ409508
Publication date: 13 April 2012
Published in: Topology and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.topol.2011.11.029
Set-valued maps in general topology (54C60) Topological spaces of dimension (leq 1); curves, dendrites (54F50) Product spaces in general topology (54B10) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80)
Related Items (17)
Tree-like continua and dendrites on set-valued inverse limits ⋮ The right homotopy shift in the fundamental groups of inverse limits ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Closed relations with non-zero entropy that generate no periodic points ⋮ Generic inverse limits with set-valued functions ⋮ The Lelek fan as the inverse limit of intervals with a single set-valued bonding function whose graph is an arc ⋮ Shift maps and their variants on inverse limits with set-valued functions ⋮ Inverse limits of set-valued functions indexed by the integers ⋮ Closed subsets of the square whose inverse limit is the Hilbert cube ⋮ Dynamical properties of shift maps on inverse limits with a set valued function ⋮ On inverse limits with set-valued functions on graphs, dimensionally stepwise spaces and ANRs ⋮ Topological entropy on closed sets in \([0,1^2\)] ⋮ Trees and generalised inverse limits on intervals ⋮ Atriodic tree-like continua as inverse limits on \([0,1\) with interval-valued functions] ⋮ Dendrites in generalized inverse limits ⋮ Inverse limits with bonding functions whose graphs are arcs
Cites Work
This page was built for publication: The only finite graph that is an inverse limit with a set valued function on \([0,1]\) is an arc
