{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/21395"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/21395","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Realcompact Alexandroff spaces and regular σ-frames","abstract":"In the early 1940's, A.D. Alexandroff [1940), [1941) and [1943] introduced a concept of space, more general than topological space, in order to obtain a simple connection between a space and the system of real-valued functions defined on it. Such a connection aided the investigation of the relationships between the linear functionals on these systems of functions and the additive set functions defined on the space. The Alexandroff spaces of this thesis are what Alexandroff himself called the completely normal spaces and what H. Gordon [1971) called the zero-set spaces.","abstract_html":"In the early 1940's, A.D. Alexandroff [1940), [1941) and [1943] introduced a concept of space, more general than topological space, in order to obtain a simple connection between a space and the system of real-valued functions defined on it. Such a connection aided the investigation of the relationships between the linear functionals on these systems of functions and the additive set functions defined on the space. The Alexandroff spaces of this thesis are what Alexandroff himself called the completely normal spaces and what H. Gordon [1971) called the zero-set spaces.","abstract_has_math":false,"creators":["Gilmour, Christopher Robert Anderson"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Brümmer, Guillaume C L"],"committee_chairs":[],"committee_members":[],"year":1981,"date_issued":"1981","date_published":"1981","updated_at":"2026-07-22T22:22:42Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/21395","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Brümmer, Guillaume C L"]},{"key":"dc:creator","label":"Author","values":["Gilmour, Christopher Robert Anderson"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-08-22T12:02:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-08-22T12:02:52Z"]},{"key":"dc:date.issued","label":"Date","values":["1981"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/21395"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 96-103."]},{"key":"dc:description.abstract","label":"Abstract","values":["In the early 1940's, A.D. Alexandroff [1940), [1941) and [1943] introduced a concept of space, more general than topological space, in order to obtain a simple connection between a space and the system of real-valued functions defined on it. Such a connection aided the investigation of the relationships between the linear functionals on these systems of functions and the additive set functions defined on the space. The Alexandroff spaces of this thesis are what Alexandroff himself called the completely normal spaces and what H. Gordon [1971) called the zero-set spaces."]},{"key":"dc:title","label":"Title","values":["Realcompact Alexandroff spaces and regular σ-frames"]}]}],"canonical_facts":{"dc:contributor.advisor":["Brümmer, Guillaume C L"],"dc:creator":["Gilmour, Christopher Robert Anderson"],"dc:date.accessioned":["2016-08-22T12:02:52Z"],"dc:date.available":["2016-08-22T12:02:52Z"],"dc:date.issued":["1981"],"dc:description":["Bibliography: pages 96-103."],"dc:description.abstract":["In the early 1940's, A.D. Alexandroff [1940), [1941) and [1943] introduced a concept of space, more general than topological space, in order to obtain a simple connection between a space and the system of real-valued functions defined on it. Such a connection aided the investigation of the relationships between the linear functionals on these systems of functions and the additive set functions defined on the space. 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