The concept of a strongly chaotic space is introduced, and its relations to chaotic, rigid and strongly rigid spaces are studied. Some sufficient as well as necessary conditions are shown for a dendrite to be strongly chaotic.
CONTENTS 1. Introduction.......................................................5 2. Preliminaries ....................................................8 3. General properties .........................................11 4. Mappings onto fans........................................14 5. Mappings onto an arc.....................................20 6. A characterization of the top...........................27 7. Open mappings and their lightness................28 8. Inverse limits...................................................39 9. Local connectedness......................................41 10. Planability......................................................43 11. Smoothness..................................................48 12. The property of Kelley...................................57 13. Contractibility................................................67 14. Selectibility....................................................77 15. Final remarks...............................................80 References.........................................................82