Generalized inverse limits and the intermediate value property.

dc.contributor.advisorRyden, David James, 1971-
dc.creatorDunn, Tavish J., 1993-
dc.creator.orcid0000-0002-0311-6776
dc.date.accessioned2022-06-14T13:33:30Z
dc.date.available2022-06-14T13:33:30Z
dc.date.created2021-08
dc.date.issued2021-07-26
dc.date.submittedAugust 2021
dc.date.updated2022-06-14T13:33:32Z
dc.description.abstractWe 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.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2104/12060
dc.language.isoen
dc.rights.accessrightsWorldwide access
dc.subjectContinuum theory. Inverse limits. Generalized inverse limits. Dynamics. Intermediate value property.
dc.titleGeneralized inverse limits and the intermediate value property.
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentBaylor University. Dept. of Mathematics.
thesis.degree.grantorBaylor University
thesis.degree.levelDoctoral
thesis.degree.namePh.D.
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