Abstract
Let f be a continuous self-mapping of a compact metric space X, an omega-limit set of f is said to be totally periodic if it is composed of periodic points. We prove that a totally periodic co-limit set of one-to-one continuous self mapping of regular continuum is finite. In the other hand, we built a continuous self-mapping (not one-to-one) of a dendrite having a totally periodic co-limit set with unbounded periods. (C) 2015 Elsevier Ltd. All rights reserved.