On light mappings of manifolds
by
E.D. Tymchatyn
University of Saskatchewan
Coauthors: Lex G.Oversteegen

Boyland has asked the following:If f is a light mapping of the plane disc to itself which is nowhere locally a homeomorphism and which maps the boundary of the disc essentially onto itself is the set of points whose preimage contains a Cantor set a dense G_\delta set?

Theorem 1. Let f from M to N be a light and weakly confluent mapping of n-manifolds. If the set of points with trivial preimage is dense in the image of f then f is an embedding.

It follows that Boyland's question has a positive answer.

Theorem 2. If f is a minimal mapping of a closed 2-manifold then f has acyclic point preimages.

Date received: June 11, 2001