Abstract
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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Doctoral
- Grantor
- Baylor University.
- Year dc:date.issued
- 2021
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Dunn, Tavish J., 1993-
- Advisor dc:contributor.advisor
-
- Ryden, David James, 1971-
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- https://hdl.handle.net/2104/12060
- OAI identifier oai:identifier
- oai:baylor-ir.tdl.org:2104/12060