{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-1176"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-1176","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"The Use Of Filters In Topology","abstract":"Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).","abstract_html":"Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).","abstract_has_math":false,"creators":["Dasser, Abdellatif"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Richardson, Gary"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-01-01T08:00:00Z","date_published":"2004-01-01T08:00:00Z","updated_at":"2026-07-24T05:08:16Z","subjects":["mathematics","topology","filters","points of closure","convergence","contnuity","compactness"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0000202"],"render_values":[{"text":"CFE0000202","href":null,"code":true}]}]},"links":{"outbound_url":"https://stars.library.ucf.edu/etd/177","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Richardson, Gary"]},{"key":"dc:creator","label":"Author","values":["Dasser, Abdellatif"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Masters Thesis (Open Access)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mathematics","topology","filters","points of closure","convergence","contnuity","compactness"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0000202"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stars.library.ucf.edu/etd/177"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Master of Science (M.S.)","College of Arts and Sciences","Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940)."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The Use Of Filters In Topology"]}]}],"canonical_facts":{"dc:contributor":["Richardson, Gary"],"dc:creator":["Dasser, Abdellatif"],"dc:description":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Master of Science (M.S.)","College of Arts and Sciences","Mathematics"],"dc:description.abstract":["Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940)."],"dc:format":["application/pdf"],"dc:identifier":["CFE0000202"],"dc:identifier.uri":["https://stars.library.ucf.edu/etd/177"],"dc:language":["English"],"dc:subject":["mathematics","topology","filters","points of closure","convergence","contnuity","compactness"],"dc:title":["The Use Of Filters In Topology"],"dc:type":["Masters Thesis (Open Access)"]},"updated_at":"2026-07-24T05:08:16Z"}