{Modifications of the Gehman dendrite}


The concept of the \g{Gehman dendrite} has been generalized in \cite[Section 4,
p. 4-10]{Arevalo+2001a} as follows.

\rostere
\item For each natural number $n \ge 3$ there exists topologically unique
dendrite $G_n$ \g{dendrite $G_n$} such that
     \rostere
\item $\mathrm{ord}\, (p, G_n) = n$ for each point $p \in R(G_n)$;
\item $E(G_n)$ is homeomorphic to the Cantor ternary set.
     \rosteree

(Note that $G_3$ is just the Gehman dendrite $G$.)

\item There exists a
\es{dendrite $G_{\omega}$}{dendrite Gomega}
such that
      \rostere
\item $\ord(p, G_{\omega})$ is finite for each point $p \in
G_{\omega}$;
\item $E(G_{\omega})$ is homeomorphic to the Cantor ternary set;
\item for each natural number $n$ and for each maximal arc $A$  contained in
$G_{\omega}$ there is a point $q \in A$ such that $\ord(q,
G_{\omega}) \ge n$.
      \rosteree

See Figure A.

\FIGURE{A}{$G_4$}

The dendrites $G_n$ and $G_{\omega}$ have the following
universality properties.

\item For each natural number $n \ge 3$ the dendrite $G_n$ is
\gs{universal}{universal dendrite} for the class of all dendrites $X$ such that
$\cl E(X) = E(X)$ and that $\ord(p,X) \le n$ for each
point $p \in X$.
\item Each dendrite $G_{\omega}$ is universal for the class of all
dendrites with the closed set of end points.
\rosteree
