{"id":{"repo_id":"baylor","oai_identifier":"oai:baylor-ir.tdl.org:2104/12060"},"canonical_url":"https://search.dev.ndltd.org/etd/baylor/oai:baylor-ir.tdl.org:2104/12060","repository":{"repo_id":"baylor","name":"Baylor University","base_url":"https://baylor-ir.tdl.org/server/oai/request"},"display":{"title":"Generalized inverse limits and the intermediate value property.","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Dunn, Tavish J., 1993-"],"institution":"Baylor University.","degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ryden, David James, 1971-"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-08","date_published":"2021-08","updated_at":"2026-07-24T01:08:21Z","subjects":["Continuum theory.","Inverse limits.","Generalized inverse limits.","Dynamics.","Intermediate value property."],"languages":["en"],"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."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2104/12060","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ryden, David James, 1971-"]},{"key":"dc:creator","label":"Author","values":["Dunn, Tavish J., 1993-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-06-14T13:33:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-06-14T13:33:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-08"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Baylor University."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Continuum theory.","Inverse limits.","Generalized inverse limits.","Dynamics.","Intermediate value property."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Baylor University works are protected by copyright. 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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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Generalized inverse limits and the intermediate value property."]}]}],"canonical_facts":{"dc:contributor.advisor":["Ryden, David James, 1971-"],"dc:creator":["Dunn, Tavish J., 1993-"],"dc:date.accessioned":["2022-06-14T13:33:30Z"],"dc:date.available":["2022-06-14T13:33:30Z"],"dc:date.issued":["2021-08"],"dc:description.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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2104/12060"],"dc:language.iso":["en"],"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."],"dc:subject":["Continuum theory.","Inverse limits.","Generalized inverse limits.","Dynamics.","Intermediate value property."],"dc:title":["Generalized inverse limits and the intermediate value property."],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["Baylor University."]},"updated_at":"2026-07-24T01:08:21Z"}