Abstract
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>
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy (PhD)
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematical Sciences
- Year
- 1975
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Robinson, Eric English
- Contributors dc:contributor
-
- Louis F. McAuley
- Patricia McAuley
- David A. Edwards
Subjects
dc:subject × 3Identifiers
dc:identifier.*- Repository record dc:identifier
- https://orb.binghamton.edu/dissertation_and_theses/289
- OAI identifier oai:identifier
- oai:orb.binghamton.edu:dissertation_and_theses-1295