THE PSEUDO-ARC

Abstract

The pseudo-arc is the simplest nondegenerate hereditarily indecomposable continuum. It is, however, also the most important, being homogeneous, having several characterizations, and having a variety of useful mapping properties. The pseudo-arc has appeared in many areas of continuum theory, as well as in several topics in geometric topology, and is beginning to make its appearance in dynamical systems. In this monograph, we give a survey of basic results and examples involving the pseudo-arc. A more complete treatment will be given in a book [133] dedicated to this topic, currently under preparation by this author. We omit formal proofs from this presentation, but do try to give indications of some basic arguments and construction techniques. Our presentation covers the following major topics. 1. Construction 2. Homogeneity 3. Characterizat ions 4. Mapping properties 5. Hyperspaces 6. Homeomorphism groups 7. Continuous decompositions 8. Dynamics