{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/21873"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/21873","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Generalized DF spaces","abstract":"A DF space is a topological vector space sharing certain essential properties with the strong duals of Frechet spaces. The class of DF spaces includes not only all such duals, but also every· normed space and many other spaces besides. The definition of a DF space is due to Grothendieck, who derived almost all the important results concerning such spaces. The \"generalized DF spaces\" in the title of this thesis are locally convex topological vector spaces whose topologies are determined by their restrictions to an absorbent sequence of bounded sets. In the case when this sequence is a fundamental sequence of bounded sets, we obtain the gDF spaces. Many. of the properties of DF spaces are shared by all gDF spaces.","abstract_html":"A DF space is a topological vector space sharing certain essential properties with the strong duals of Frechet spaces. The class of DF spaces includes not only all such duals, but also every· normed space and many other spaces besides. The definition of a DF space is due to Grothendieck, who derived almost all the important results concerning such spaces. The "generalized DF spaces" in the title of this thesis are locally convex topological vector spaces whose topologies are determined by their restrictions to an absorbent sequence of bounded sets. In the case when this sequence is a fundamental sequence of bounded sets, we obtain the gDF spaces. Many. of the properties of DF spaces are shared by all gDF spaces.","abstract_has_math":false,"creators":["Robertson, Neill Raymond Charles"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Webb, John H"],"committee_chairs":[],"committee_members":[],"year":1984,"date_issued":"1984","date_published":"1984","updated_at":"2026-07-22T22:23:05Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/21873","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Webb, John H"]},{"key":"dc:creator","label":"Author","values":["Robertson, Neill Raymond Charles"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-09-25T16:18:50Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-09-25T16:18:50Z"]},{"key":"dc:date.issued","label":"Date","values":["1984"]},{"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":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"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/11427/21873"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 102-106."]},{"key":"dc:description.abstract","label":"Abstract","values":["A DF space is a topological vector space sharing certain essential properties with the strong duals of Frechet spaces. The class of DF spaces includes not only all such duals, but also every· normed space and many other spaces besides. The definition of a DF space is due to Grothendieck, who derived almost all the important results concerning such spaces. The \"generalized DF spaces\" in the title of this thesis are locally convex topological vector spaces whose topologies are determined by their restrictions to an absorbent sequence of bounded sets. In the case when this sequence is a fundamental sequence of bounded sets, we obtain the gDF spaces. Many. of the properties of DF spaces are shared by all gDF spaces."]},{"key":"dc:title","label":"Title","values":["Generalized DF spaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Webb, John H"],"dc:creator":["Robertson, Neill Raymond Charles"],"dc:date.accessioned":["2016-09-25T16:18:50Z"],"dc:date.available":["2016-09-25T16:18:50Z"],"dc:date.issued":["1984"],"dc:description":["Bibliography: pages 102-106."],"dc:description.abstract":["A DF space is a topological vector space sharing certain essential properties with the strong duals of Frechet spaces. The class of DF spaces includes not only all such duals, but also every· normed space and many other spaces besides. The definition of a DF space is due to Grothendieck, who derived almost all the important results concerning such spaces. The \"generalized DF spaces\" in the title of this thesis are locally convex topological vector spaces whose topologies are determined by their restrictions to an absorbent sequence of bounded sets. In the case when this sequence is a fundamental sequence of bounded sets, we obtain the gDF spaces. Many. of the properties of DF spaces are shared by all gDF spaces."],"dc:identifier.uri":["http://hdl.handle.net/11427/21873"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Generalized DF spaces"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:05Z"}