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    Generalized inverse limits and the intermediate value property.

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    DUNN-DISSERTATION-2021.pdf (1018.Kb)
    Tavish_Dunn_copyrightavailabilityform.pdf (333.5Kb)
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    Date
    2021-07-26
    Author
    Dunn, Tavish J., 1993-
    0000-0002-0311-6776
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    Abstract
    We introduce and discuss various notions of the intermediate value property applicable to upper-semicontinuous set-valued functions f : [0, 1] → 2^[0,1]. In the first part, we present sufficient conditions such that an inverse limit of a sequence of bonding functions of this type is a continuum. In the second part, we examine the relationship between the dynamics of an upper-semicontinuous function with the intermediate value property and the topological structure of the corresponding inverse limit. In particular, we present conditions under which the existence of a cycle of period not a power of 2 implies indecomposability in the inverse limit and vice-versa. Lastly, we show that these conditions are sharp by constructing a family of upper-semicontinuous functions with the intermediate value property and cycles of all periods, yet admits a hereditarily decomposable inverse limit.
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    https://hdl.handle.net/2104/12060
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    Copyright © Baylor® University All rights reserved. Legal Disclosures.
    Baylor University Waco, Texas 76798 1-800-BAYLOR-U
    Baylor University Libraries | One Bear Place #97148 | Waco, TX 76798-7148 | 254.710.2112 | Contact: libraryquestions@baylor.edu
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    DSpace software copyright © 2002-2016  DuraSpace
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