## Document Type

Dissertation

## Date of Award

1975

## Keywords

Conformal mapping, Homotopy theory, Manifolds (Mathematics)

## Degree Name

Doctor of Philosophy (PhD)

## Department

Mathematical Sciences

## First Advisor

Louis F. McAuley

## Second Advisor

Patricia McAuley

## Third Advisor

David A. Edwards

## Abstract

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:

*Theorem*. 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^{-1}(f(B_{f})) is a regular covering where B_{f} is the set of points at which f fails to be a local homeomorphism.

This generalizes a result of Edmonds (Branched Coverings and the Geometry of n - circuits, to appear.)

## Recommended Citation

Robinson, Eric English, "Characterization and properties of some light-open mappings" (1975). *Graduate Dissertations and Theses*. 289.

https://orb.binghamton.edu/dissertation_and_theses/289