We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.
","abstract_html":"<p>We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.</p>","abstract_has_math":false,"creators":["Trott, William D"],"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":["Jimmy Dillies","Greg Michalski"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:52Z","subjects":["ETD","Regularity","Continuous extension","Continuous convergence","Other Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1095","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jimmy Dillies","Greg Michalski"]},{"key":"dc:creator","label":"Author","values":["Trott, William D"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-04-13T07:00:00Z"]},{"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","Regularity","Continuous extension","Continuous convergence","Other Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1095"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.
"]},{"key":"dc:title","label":"Title","values":["Elements of Convergence Approach Theory"]}]}],"canonical_facts":{"dc:contributor":["Jimmy Dillies","Greg Michalski"],"dc:creator":["Trott, William D"],"dc:date.available":["2014-04-13T07:00:00Z"],"dc:description.abstract":["We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.
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