This thesis deals primarily with decomposition spaces and the question of inheritance by a decomposition space of certain topological properties. Some new topological concepts which are introduced are of independent interest but they are explored here principally for their implications in decomposition spaces.
In Chapter II we compare McAuley's definition of an upper semicontinuous decomposition with other separation properties of the decomposition space and relations of these properties to the projection map. In contrast to Whyburn's (originally, Moore's) definition of upper semicontinuity, which is equivalent to requiring the projection map to be closed, these are purely topological properties, but some nevertheless impose conditions on quotient maps onto spaces satisfying them. Also, they are investigated in conjunction with various basis restrictions on the decomposition space (such as first countability, etc.) or conditions on the nature of the individual elements of the decomposition.
Chapter III is more narrow in scope, dealing specifically with certain shrinkability theorems of McAuley, originally asserted for decompositions which are upper semicontinuous in the sense he defined. The observation that this definition of upper semicontinuity did not yield the desired properties as supposed led to the investigations of Chapter II. Proofs of the theorems with the amended hypotheses are supplied.
","abstract_html":"<p>This thesis deals primarily with decomposition spaces and the question of inheritance by a decomposition space of certain topological properties. Some new topological concepts which are introduced are of independent interest but they are explored here principally for their implications in decomposition spaces.</p> <p>In Chapter II we compare McAuley's definition of an upper semicontinuous decomposition with other separation properties of the decomposition space and relations of these properties to the projection map. In contrast to Whyburn's (originally, Moore's) definition of upper semicontinuity, which is equivalent to requiring the projection map to be closed, these are purely topological properties, but some nevertheless impose conditions on quotient maps onto spaces satisfying them. Also, they are investigated in conjunction with various basis restrictions on the decomposition space (such as first countability, etc.) or conditions on the nature of the individual elements of the decomposition.</p> <p>Chapter III is more narrow in scope, dealing specifically with certain shrinkability theorems of McAuley, originally asserted for decompositions which are upper semicontinuous in the sense he defined. The observation that this definition of upper semicontinuity did not yield the desired properties as supposed led to the investigations of Chapter II. Proofs of the theorems with the amended hypotheses are supplied.</p>","abstract_has_math":false,"creators":["Reed, Myra Jean"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Louis F. McAuley","Dick Wick Hall","Hudson V. Kronk"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1971,"date_issued":"1971-01-01T08:00:00Z","date_published":"1971-01-01T08:00:00Z","updated_at":"2026-07-24T01:10:16Z","subjects":["Topology","Decomposition spaces","Separation properties"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://orb.binghamton.edu/dissertation_and_theses/169","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Louis F. McAuley","Dick Wick Hall","Hudson V. Kronk"]},{"key":"dc:creator","label":"Author","values":["Reed, Myra Jean"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Topology","Decomposition spaces","Separation properties"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://orb.binghamton.edu/dissertation_and_theses/169"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis deals primarily with decomposition spaces and the question of inheritance by a decomposition space of certain topological properties. Some new topological concepts which are introduced are of independent interest but they are explored here principally for their implications in decomposition spaces.
In Chapter II we compare McAuley's definition of an upper semicontinuous decomposition with other separation properties of the decomposition space and relations of these properties to the projection map. In contrast to Whyburn's (originally, Moore's) definition of upper semicontinuity, which is equivalent to requiring the projection map to be closed, these are purely topological properties, but some nevertheless impose conditions on quotient maps onto spaces satisfying them. Also, they are investigated in conjunction with various basis restrictions on the decomposition space (such as first countability, etc.) or conditions on the nature of the individual elements of the decomposition.
Chapter III is more narrow in scope, dealing specifically with certain shrinkability theorems of McAuley, originally asserted for decompositions which are upper semicontinuous in the sense he defined. The observation that this definition of upper semicontinuity did not yield the desired properties as supposed led to the investigations of Chapter II. Proofs of the theorems with the amended hypotheses are supplied.
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In Chapter II we compare McAuley's definition of an upper semicontinuous decomposition with other separation properties of the decomposition space and relations of these properties to the projection map. In contrast to Whyburn's (originally, Moore's) definition of upper semicontinuity, which is equivalent to requiring the projection map to be closed, these are purely topological properties, but some nevertheless impose conditions on quotient maps onto spaces satisfying them. Also, they are investigated in conjunction with various basis restrictions on the decomposition space (such as first countability, etc.) or conditions on the nature of the individual elements of the decomposition.
Chapter III is more narrow in scope, dealing specifically with certain shrinkability theorems of McAuley, originally asserted for decompositions which are upper semicontinuous in the sense he defined. The observation that this definition of upper semicontinuity did not yield the desired properties as supposed led to the investigations of Chapter II. Proofs of the theorems with the amended hypotheses are supplied.
"],"dc:identifier":["https://orb.binghamton.edu/dissertation_and_theses/169"],"dc:subject":["Topology","Decomposition spaces","Separation properties"],"dc:title":["Decomposition spaces and separation properties"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T01:10:16Z"}