{Gehman dendrite}

One of the classical examples of dendrites with its set of
end points closed is the
\e{Gehman dendrite}
.
It can be described as a dendrite $G$ having the
set $E(G)$ homeomorphic to the Cantor ternary set $C$ in
$[0,1]$ such that all ramification points of $G$ are of
order 3 (see \cite[the example on p. 42]{Gehman1925a}; see
also \cite[p. 422-423]{Nikiel1983a} for a geometrical
description; compare \cite[p. 82]{Nikiel1989a} and
\cite[Example 10.39, p. 186]{Nadler1992a}).
See Figure A.

\FIGURE{A}{Gehman dendrite}

%PP: put, please a picture of the Gehman dendrite here.

The Gehman dendrite has the following properties.
\rostere
\item The set $R(G)$ of all ramification points of $G$ is discrete.
\item $E(G) = \cl(R(G)) \setminus R(G)$.
\item Each dendrite with an uncountable set of its end points contains
a homeomorphic copy of the Gehman dendrite, \cite[Proposition 6.8, p.
16]{Arevalo+2001a}.

%A space $X$ is said to have the \g{periodic-recurrent property}
%\g{periodic-recurrent property} provided that for each mapping $f: X
%\to X$ the closures of the sets of periodic and of recurrent points of $f$
%are equal (see \cite[Definition 1.2, p. 109]{Charatonik+1997b}). The following results
%are known.

\item If a continuum contains the Gehman dendrite, then it does not
have the \g{periodic-recurrent
property}, \cite[Theorem 3.3, p. 136]{Charatonik1998a}.
\item A dendrite $X$ contains the Gehman dendrite if and only if $X$
does not have the periodic-recurrent property,
\cite[Theorem 2, p. 222]{Illanes1998a}.
\rosteree
