cyclic element

Let a continuum X be locally connected and let $p \in X$. By a cyclic element of X containing p we mean either the singleton {p} if p is a cut point or an end point of X, or the set consisting of p and of all points $x \in X$ such that no point of X cuts X between p and x, otherwise (see e.g. [78, Chapter 4, §2, p. 66]).