Connected partitions of continua into compacta
by
Francis Jordan
Georgia Southern University

We consider partitions Q of a continuum X into compacta such that Q is a connected set in the hyperspace of nonempty compact subsets of X. Such partitions naturally arise from open mappings and in the study of continuous selections. We say a continuum X has the property P provided that every connected partition of X is compact. Dendrites have property P. A graph X has property P if and only if X is a tree or a simple closed curve. We give two examples that show that the continua with property P may be hard to characterize in general.

Date received: February 20, 2006