Some results about inverse limits with set-valued bonding functions

In the paper, we give new results about dimension of inverse limits with upper semicontinuous bonding functions. We also construct an upper semicontinuous function f:[0,1]→2[0,1] with the following properties: (1) the graph of f is an arc, (2) the graph of f is surjective, (3) the inverse limit lim←...

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Bibliographic Details
Published in:Topology and its applications 2016-04, Vol.202, p.106-111
Main Authors: Banič, Iztok, Črepnjak, Matevž, Nall, Van
Format: Article
Language:English
Subjects:
Arcs
Continua
Dimension
Inverse limits
Upper semicontinuous functions
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Summary:In the paper, we give new results about dimension of inverse limits with upper semicontinuous bonding functions. We also construct an upper semicontinuous function f:[0,1]→2[0,1] with the following properties: (1) the graph of f is an arc, (2) the graph of f is surjective, (3) the inverse limit lim←{[0,1],f}n=1∞ contains a simple closed curve, and (4) the dimension of lim←{[0,1],f}n=1∞ is 1. This answers a question by W.T. Ingram.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2016.01.007