The Closed Subset Theorem for Inverse Limits with Upper Semicontinuous Bonding Functions

We give several characterizations of inverse limits of compact metric spaces with upper semicontinuous set-valued bonding functions having the property that any closed subset of the inverse limit is the inverse limit of its projections. This solves a problem stated by Ingram.

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2019-05, Vol.42 (3), p.835-846
Main Authors: Banič, Iztok, Črepnjak, Matevž, Merhar, Matej, Milutinović, Uroš, Sovič, Tina
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:We give several characterizations of inverse limits of compact metric spaces with upper semicontinuous set-valued bonding functions having the property that any closed subset of the inverse limit is the inverse limit of its projections. This solves a problem stated by Ingram.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-017-0517-5