{"id":{"repo_id":"binghamton","oai_identifier":"oai:orb.binghamton.edu:dissertation_and_theses-1295"},"canonical_url":"https://search.dev.ndltd.org/etd/binghamton/oai:orb.binghamton.edu:dissertation_and_theses-1295","repository":{"repo_id":"binghamton","name":"Binghamton University","base_url":"https://orb.binghamton.edu/do/oai/"},"display":{"title":"Characterization and properties of some light-open mappings","abstract":"<p>We prove the converse of a theorem of McAuley (TOPO - 72 - General Topology and its Applications, Proc. 1972. Springer Lecture Notes, Vol. 378) and thus complete a characterization of light-open mappings between Peano continua by a sequence of special coverings of the domain. We also prove some covering homotopy theorems for a certain class of finite-to-one open maps and show that a classifying space exists for maps in this class, where point inverses consist of either n points or one point, provided a certain type of covering space exists. In addition, we have the following corollary to our work:</p> <p><em>Theorem</em>. A finite-to-one proper open map f:X ⇒Y between connected separable n-manifolds without boundary is the orbit map of a group action if and only if f|x - f<sup>-1</sup>(f(B<sub>f</sub>)) is a regular covering where B<sub>f</sub> is the set of points at which f fails to be a local homeomorphism.</p> <p>This generalizes a result of Edmonds (Branched Coverings and the Geometry of n - circuits, to appear.)</p>","abstract_html":"&lt;p&gt;We prove the converse of a theorem of McAuley (TOPO - 72 - General Topology and its Applications, Proc. 1972. Springer Lecture Notes, Vol. 378) and thus complete a characterization of light-open mappings between Peano continua by a sequence of special coverings of the domain. We also prove some covering homotopy theorems for a certain class of finite-to-one open maps and show that a classifying space exists for maps in this class, where point inverses consist of either n points or one point, provided a certain type of covering space exists. In addition, we have the following corollary to our work:&lt;/p&gt; &lt;p&gt;&lt;em&gt;Theorem&lt;/em&gt;. A finite-to-one proper open map f:X ⇒Y between connected separable n-manifolds without boundary is the orbit map of a group action if and only if f|x - f&lt;sup&gt;-1&lt;/sup&gt;(f(B&lt;sub&gt;f&lt;/sub&gt;)) is a regular covering where B&lt;sub&gt;f&lt;/sub&gt; is the set of points at which f fails to be a local homeomorphism.&lt;/p&gt; &lt;p&gt;This generalizes a result of Edmonds (Branched Coverings and the Geometry of n - circuits, to appear.)&lt;/p&gt;","abstract_has_math":false,"creators":["Robinson, Eric English"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Louis F. McAuley","Patricia McAuley","David A. Edwards"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1975,"date_issued":"1975-01-01T08:00:00Z","date_published":"1975-01-01T08:00:00Z","updated_at":"2026-07-24T01:10:35Z","subjects":["Conformal mapping","Homotopy theory","Manifolds (Mathematics)"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://orb.binghamton.edu/dissertation_and_theses/289","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Louis F. McAuley","Patricia McAuley","David A. Edwards"]},{"key":"dc:creator","label":"Author","values":["Robinson, Eric English"]}]},{"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":["Conformal mapping","Homotopy theory","Manifolds (Mathematics)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://orb.binghamton.edu/dissertation_and_theses/289"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We prove the converse of a theorem of McAuley (TOPO - 72 - General Topology and its Applications, Proc. 1972. Springer Lecture Notes, Vol. 378) and thus complete a characterization of light-open mappings between Peano continua by a sequence of special coverings of the domain. We also prove some covering homotopy theorems for a certain class of finite-to-one open maps and show that a classifying space exists for maps in this class, where point inverses consist of either n points or one point, provided a certain type of covering space exists. In addition, we have the following corollary to our work:</p> <p><em>Theorem</em>. A finite-to-one proper open map f:X ⇒Y between connected separable n-manifolds without boundary is the orbit map of a group action if and only if f|x - f<sup>-1</sup>(f(B<sub>f</sub>)) is a regular covering where B<sub>f</sub> is the set of points at which f fails to be a local homeomorphism.</p> <p>This generalizes a result of Edmonds (Branched Coverings and the Geometry of n - circuits, to appear.)</p>"]},{"key":"dc:title","label":"Title","values":["Characterization and properties of some light-open mappings"]}]}],"canonical_facts":{"dc:contributor":["Louis F. McAuley","Patricia McAuley","David A. Edwards"],"dc:creator":["Robinson, Eric English"],"dc:description.abstract":["<p>We prove the converse of a theorem of McAuley (TOPO - 72 - General Topology and its Applications, Proc. 1972. Springer Lecture Notes, Vol. 378) and thus complete a characterization of light-open mappings between Peano continua by a sequence of special coverings of the domain. We also prove some covering homotopy theorems for a certain class of finite-to-one open maps and show that a classifying space exists for maps in this class, where point inverses consist of either n points or one point, provided a certain type of covering space exists. In addition, we have the following corollary to our work:</p> <p><em>Theorem</em>. A finite-to-one proper open map f:X ⇒Y between connected separable n-manifolds without boundary is the orbit map of a group action if and only if f|x - f<sup>-1</sup>(f(B<sub>f</sub>)) is a regular covering where B<sub>f</sub> is the set of points at which f fails to be a local homeomorphism.</p> <p>This generalizes a result of Edmonds (Branched Coverings and the Geometry of n - circuits, to appear.)</p>"],"dc:identifier":["https://orb.binghamton.edu/dissertation_and_theses/289"],"dc:subject":["Conformal mapping","Homotopy theory","Manifolds (Mathematics)"],"dc:title":["Characterization and properties of some light-open mappings"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T01:10:35Z"}