The relationship between k-fold covering maps and
by
Randall Griffus
Auburn University and Dalton College

Recently, J. Heath proved that every 2-crisp map is a 2-fold covering map and that every 2-fold covering map has a 2-crisp restriction to a subcontinuum. She then asked about the relationship if 2 is replaced by an integer k greater than 2. We show that every k-crisp map is a k-fold cover and, for every k greater than 2, we construct a k-fold covering map which does not have a k-crisp restriction to a subcontinuum.

A map is k-crisp if the domain is a continuum and for each proper subcontinuum C of the image, the inverse of C consists of k disjoint continua, each of which is mapped homeomorphically onto C.

Date received: January 17, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-02.