Abstract:
A continuum X has the Omega - EP property provided that for each self-mapping f the set of nonwandering points of f is contained in the closure of the set of eventually periodic points of f. It is known that the interval and some other continua have the Omega - EP property. We show in this note that the sin(1/x)-continuum does not have this property. (c) 2007 Elsevier B.V. All rights reserved.