{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/14380"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/14380","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Realcompactifications of frames","abstract":"The first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications.","abstract_html":"The first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications.","abstract_has_math":false,"creators":["Marcus, Nizar"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Gilmour, Christopher Robert Anderson"],"committee_chairs":[],"committee_members":[],"year":1993,"date_issued":"1993","date_published":"1993","updated_at":"2026-07-22T22:23:12Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/14380","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gilmour, Christopher Robert Anderson"]},{"key":"dc:creator","label":"Author","values":["Marcus, Nizar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-10-28T05:29:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-10-28T05:29:53Z"]},{"key":"dc:date.issued","label":"Date","values":["1993"]},{"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/11427/14380"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: leaves 53-57."]},{"key":"dc:description.abstract","label":"Abstract","values":["The first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications."]},{"key":"dc:title","label":"Title","values":["Realcompactifications of frames"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gilmour, Christopher Robert Anderson"],"dc:creator":["Marcus, Nizar"],"dc:date.accessioned":["2015-10-28T05:29:53Z"],"dc:date.available":["2015-10-28T05:29:53Z"],"dc:date.issued":["1993"],"dc:description":["Bibliography: leaves 53-57."],"dc:description.abstract":["The first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications."],"dc:identifier.uri":["http://hdl.handle.net/11427/14380"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Realcompactifications of frames"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:12Z"}