A Cyclic Element Characterization of Monotone Normality
by
Dale Daniel
Lamar University
Coauthors: L. B. Treybig

A subcontinuum g of a locally connected continuum X is a cyclic element of X provided that g is maximal with respect to the property that no point separates it. If, in addition, g is non-degenerate, g is called a true cyclic element of X. In an earlier paper, Cornette showed that a locally connected continuum X is the continuous image of an arc if and only if each cyclic element of X is the continuous image of an arc. In this paper, we prove the analogous result for monotonically normal continua by showing that a locally connected continuum X is monotonically normal if and only if each cyclic element of X is monotonically normal.

Date received: January 28, 1999

Copyright © 1999 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 # caca-19.