{"id":{"repo_id":"wvu","oai_identifier":"oai:researchrepository.wvu.edu:etd-1387"},"canonical_url":"https://search.dev.ndltd.org/etd/wvu/oai:researchrepository.wvu.edu:etd-1387","repository":{"repo_id":"wvu","name":"West Virginia University","base_url":"https://researchrepository.wvu.edu/do/oai/"},"display":{"title":"Continuities on Subspaces","abstract":"We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S , describe the sets of discontinuities of such functions (characterizing several classes), and discuss the regularity of such functions.","abstract_html":"We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S , describe the sets of discontinuities of such functions (characterizing several classes), and discuss the regularity of such functions.","abstract_has_math":false,"creators":["Glatzer, Timothy James"],"institution":null,"degree_name":"PhD","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Krzysztof Ciesielski","Edgar Fuller","John Goldwasser","Robert Mnatsakanov","Jerzy Wojciechowski"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-12-01T08:00:00Z","date_published":"2013-12-01T08:00:00Z","updated_at":"2026-07-24T06:14:24Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://researchrepository.wvu.edu/etd/384"],"render_values":[{"text":"https://researchrepository.wvu.edu/etd/384","href":"https://researchrepository.wvu.edu/etd/384","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.33915/etd.384","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Krzysztof Ciesielski","Edgar Fuller","John Goldwasser","Robert Mnatsakanov","Jerzy Wojciechowski"]},{"key":"dc:creator","label":"Author","values":["Glatzer, Timothy James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-01-17T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.33915/etd.384","https://researchrepository.wvu.edu/etd/384"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S , describe the sets of discontinuities of such functions (characterizing several classes), and discuss the regularity of such functions."]},{"key":"dc:title","label":"Title","values":["Continuities on Subspaces"]}]}],"canonical_facts":{"dc:contributor":["Krzysztof Ciesielski","Edgar Fuller","John Goldwasser","Robert Mnatsakanov","Jerzy Wojciechowski"],"dc:creator":["Glatzer, Timothy James"],"dc:date.available":["2019-01-17T08:00:00Z"],"dc:description.abstract":["We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S , describe the sets of discontinuities of such functions (characterizing several classes), and discuss the regularity of such functions."],"dc:identifier":["https://doi.org/10.33915/etd.384","https://researchrepository.wvu.edu/etd/384"],"dc:subject":["Mathematics"],"dc:title":["Continuities on Subspaces"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["PhD"]},"updated_at":"2026-07-24T06:14:24Z"}