On λ-Dendroids with the ΩEP-Property

Abstract

A space X has the ΩEP-property if for each self-mapping the set of nonwandering points is contained in the closure of the set of eventually periodic points. A class of λ-dendroids is presented each member of which has the ΩEP-property for mappings satisfying certain additional conditions. These λ-dendroids are obtained as compactifications of some dendrites without finite sets. Some related problems are posed.

Keywords:

• Compactification
• continuum
• dendrite
• eventually periodic point
• λ-dendroid
• mapping
• nonwandering point
• periodic point
• recurrent point