Big and large continua in inverse limits of inverse systems over directed graphs

In the theory of generalized inverse limits it is a well-known fact that the generalized inverse limits may not be connected even if all the factor spaces are closed intervals. However, it has been shown recently by Banič and Kennedy that such generalized inverse limits always contain large continua...

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Bibliographic Details
Published in:Topology and its applications 2020-04, Vol.274, p.107119, Article 107119
Main Authors: Banič, Iztok, Črepnjak, Matevž, Goričan, Peter, Kac, Teja, Merhar, Matej, Milutinović, Uroš
Format: Article
Language:English
Subjects:
Big continua
Directed graphs
Inverse limits
Large continua
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Summary:In the theory of generalized inverse limits it is a well-known fact that the generalized inverse limits may not be connected even if all the factor spaces are closed intervals. However, it has been shown recently by Banič and Kennedy that such generalized inverse limits always contain large continua, if the bonding functions have connected and surjective graphs. We generalize the notion of generalized inverse limits of inverse sequences of closed intervals with upper semicontinuous bonding functions to inverse limits of inverse systems over directed graphs and show that under certain conditions, such inverse limits also contain large continua.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2020.107119