{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1675"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1675","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Compact Filters and the Arzelá-Ascoli Theorem","abstract":"The Arzelà-Ascoli Theorem gives conditions for a set to be compact in a function space, and is a useful theorem for existence proofs in many different mathematical contexts. The most natural structure for Arzelà-Ascoli type theorems is the continuous convergence - which is not necessarily topological even if the underlying base spaces are. Compact filters, on the other hand, are the logical extension of compact sets to filters with similar compactness-type properties. Compact filters have proved to be a useful tool in optimization and analysis. This thesis will show conditions for a filter to be compact on a function space, thus establishing an Arzelà-Ascoli type of result for filters.","abstract_html":"The Arzelà-Ascoli Theorem gives conditions for a set to be compact in a function space, and is a useful theorem for existence proofs in many different mathematical contexts. The most natural structure for Arzelà-Ascoli type theorems is the continuous convergence - which is not necessarily topological even if the underlying base spaces are. Compact filters, on the other hand, are the logical extension of compact sets to filters with similar compactness-type properties. Compact filters have proved to be a useful tool in optimization and analysis. This thesis will show conditions for a filter to be compact on a function space, thus establishing an Arzelà-Ascoli type of result for filters.","abstract_has_math":false,"creators":["Farmer, Nathan Denton"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Greg Michalski","Goran Lesaja"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-01T07:00:00Z","date_published":"2012-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Arzelá-Ascoli","Compact filters","Convergence spaces","Function spaces","Filters","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/675","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Greg Michalski","Goran Lesaja"]},{"key":"dc:creator","label":"Author","values":["Farmer, Nathan Denton"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Arzelá-Ascoli","Compact filters","Convergence spaces","Function spaces","Filters","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/675"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Arzelà-Ascoli Theorem gives conditions for a set to be compact in a function space, and is a useful theorem for existence proofs in many different mathematical contexts. The most natural structure for Arzelà-Ascoli type theorems is the continuous convergence - which is not necessarily topological even if the underlying base spaces are. Compact filters, on the other hand, are the logical extension of compact sets to filters with similar compactness-type properties. Compact filters have proved to be a useful tool in optimization and analysis. This thesis will show conditions for a filter to be compact on a function space, thus establishing an Arzelà-Ascoli type of result for filters."]},{"key":"dc:title","label":"Title","values":["Compact Filters and the Arzelá-Ascoli Theorem"]}]}],"canonical_facts":{"dc:contributor":["Greg Michalski","Goran Lesaja"],"dc:creator":["Farmer, Nathan Denton"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["The Arzelà-Ascoli Theorem gives conditions for a set to be compact in a function space, and is a useful theorem for existence proofs in many different mathematical contexts. The most natural structure for Arzelà-Ascoli type theorems is the continuous convergence - which is not necessarily topological even if the underlying base spaces are. Compact filters, on the other hand, are the logical extension of compact sets to filters with similar compactness-type properties. Compact filters have proved to be a useful tool in optimization and analysis. This thesis will show conditions for a filter to be compact on a function space, thus establishing an Arzelà-Ascoli type of result for filters."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/675"],"dc:subject":["ETD","Arzelá-Ascoli","Compact filters","Convergence spaces","Function spaces","Filters","Mathematics"],"dc:title":["Compact Filters and the Arzelá-Ascoli Theorem"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}