Simple Techniques for Detecting Decomposability or Indecomposability of Generalized Inverse Limits

Abstract

A continuum X is said to be decomposable if it can be written as a union of two proper subcontinua; otherwise, X is said to be indecomposable. For years, topologists have used inverse limits with continuous bonding functions to study indecomposable continua. Now that the topic of generalized inverse limits with upper semi-continuous (or ''u.s.c.'') bonding functions has become popular, it is natural to consider how these new kinds of inverse limits might be used to generate indecomposable (or decomposable) continua.

In this work, we build upon our past results (from ''Inverse Limits with Upper Semi-Continuous Bonding Functions and Indecomposability'') to obtain new and more general theorems about how to generate indecomposable (or decomposable) continua from u.s.c. inverse limits. In particular, we seek sufficient conditions for indecomposability (or decomposability) that are easily checked, just from a straightforward observation of the bonding functions of the inverse limit. Our primary focus is the case of inverse limits whose factor spaces are indexed by the positive integers, but we consider extensions to other cases as well.