{"id":{"repo_id":"uab","oai_identifier":"oai:digitalcommons.library.uab.edu:etd-collection-7968"},"canonical_url":"https://search.dev.ndltd.org/etd/uab/oai:digitalcommons.library.uab.edu:etd-collection-7968","repository":{"repo_id":"uab","name":"University of Alabama Birmingham","base_url":"https://digitalcommons.library.uab.edu/do/oai/"},"display":{"title":"Concerning the Covering Theorem for Closed and Perfectly Compact Point Sets.","abstract":"In this thesis it will be shown that, as a consequence of R. L. Moore’s Axiom 0 and the Well-Ordering Theorem, the following is a theorem: If M is a closed point set, then M is perfectly compact if, and only if, when G is a collection of regions covering M, then some finite subcollection of G covers M. ","abstract_html":"In this thesis it will be shown that, as a consequence of R. L. Moore’s Axiom 0 and the Well-Ordering Theorem, the following is a theorem: If M is a closed point set, then M is perfectly compact if, and only if, when G is a collection of regions covering M, then some finite subcollection of G covers M. ","abstract_has_math":false,"creators":["Nix, Thomas Leon"],"institution":null,"degree_name":null,"degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1974,"date_issued":"1974-01-01T08:00:00Z","date_published":"1974-01-01T08:00:00Z","updated_at":"2026-07-24T05:05:33Z","subjects":["Closed point sets","Well-Ordering Theorem","Compact point sets"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.library.uab.edu/etd-collection/6976","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Nix, Thomas Leon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Closed point sets","Well-Ordering Theorem","Compact point sets"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.library.uab.edu/etd-collection/6976"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis it will be shown that, as a consequence of R. L. Moore’s Axiom 0 and the Well-Ordering Theorem, the following is a theorem: If M is a closed point set, then M is perfectly compact if, and only if, when G is a collection of regions covering M, then some finite subcollection of G covers M. "]},{"key":"dc:title","label":"Title","values":["Concerning the Covering Theorem for Closed and Perfectly Compact Point Sets."]}]}],"canonical_facts":{"dc:creator":["Nix, Thomas Leon"],"dc:description.abstract":["In this thesis it will be shown that, as a consequence of R. L. Moore’s Axiom 0 and the Well-Ordering Theorem, the following is a theorem: If M is a closed point set, then M is perfectly compact if, and only if, when G is a collection of regions covering M, then some finite subcollection of G covers M. "],"dc:identifier":["https://digitalcommons.library.uab.edu/etd-collection/6976"],"dc:subject":["Closed point sets","Well-Ordering Theorem","Compact point sets"],"dc:title":["Concerning the Covering Theorem for Closed and Perfectly Compact Point Sets."],"thesis:degree_level":["Thesis"]},"updated_at":"2026-07-24T05:05:33Z"}