{"id":{"repo_id":"must-thes","oai_identifier":"oai:scholarsmine.mst.edu:doctoral_dissertations-1193"},"canonical_url":"https://search.dev.ndltd.org/etd/must-thes/oai:scholarsmine.mst.edu:doctoral_dissertations-1193","repository":{"repo_id":"must-thes","name":"Missouri University of Science and Technology","base_url":"https://scholarsmine.mst.edu/do/oai/"},"display":{"title":"Some results on quasi-uniform spaces","abstract":"<p>\"An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T<sub>1</sub> space does not necessarily have a T<sub>1</sub> strong completion.</p> <p>The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.</p> <p>Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is proved. The generation of the fine quasi-uniform structure is discussed.</p> <p>A general method for constructing compatible quasi-uniform structures is obtained. It is shown that the method can be applied to obtain a compatible non-transitive quasi-uniform structure as well as any compatible transitive quasi-uniform structure\"--Abstract, page iii.</p>","abstract_html":"&lt;p&gt;&quot;An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T&lt;sub&gt;1&lt;/sub&gt; space does not necessarily have a T&lt;sub&gt;1&lt;/sub&gt; strong completion.&lt;/p&gt; &lt;p&gt;The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.&lt;/p&gt; &lt;p&gt;Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is proved. The generation of the fine quasi-uniform structure is discussed.&lt;/p&gt; &lt;p&gt;A general method for constructing compatible quasi-uniform structures is obtained. It is shown that the method can be applied to obtain a compatible non-transitive quasi-uniform structure as well as any compatible transitive quasi-uniform structure&quot;--Abstract, page iii.&lt;/p&gt;","abstract_has_math":false,"creators":["Carter, Karen Sylvia"],"institution":"University of Missouri--Rolla","degree_name":"Ph. D. in Mathematics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:20:02Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/191","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Carter, Karen Sylvia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Rolla"]}]},{"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://scholarsmine.mst.edu/doctoral_dissertations/191"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>\"An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T<sub>1</sub> space does not necessarily have a T<sub>1</sub> strong completion.</p> <p>The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.</p> <p>Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is proved. The generation of the fine quasi-uniform structure is discussed.</p> <p>A general method for constructing compatible quasi-uniform structures is obtained. It is shown that the method can be applied to obtain a compatible non-transitive quasi-uniform structure as well as any compatible transitive quasi-uniform structure\"--Abstract, page iii.</p>"]},{"key":"dc:title","label":"Title","values":["Some results on quasi-uniform spaces"]}]}],"canonical_facts":{"dc:creator":["Carter, Karen Sylvia"],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["<p>\"An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T<sub>1</sub> space does not necessarily have a T<sub>1</sub> strong completion.</p> <p>The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.</p> <p>Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is proved. The generation of the fine quasi-uniform structure is discussed.</p> <p>A general method for constructing compatible quasi-uniform structures is obtained. It is shown that the method can be applied to obtain a compatible non-transitive quasi-uniform structure as well as any compatible transitive quasi-uniform structure\"--Abstract, page iii.</p>"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/191"],"dc:subject":["Mathematics"],"dc:title":["Some results on quasi-uniform spaces"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Mathematics"],"thesis:institution_name":["University of Missouri--Rolla"]},"updated_at":"2026-07-24T03:20:02Z"}