{The locally connected combs}
\label{ex-lccombs}
The next two
examples are defined in \cite[p. 3]{Arevalo+2001a}. Let
$\overline {pq}$ stand for the straight line segment from
$p$ to $q$ in the plane. In the plane, let $a = (0,0), a_n =
(1/n, 1/n), b_n = (1/n, 0)$ for each $n \in
\mathbb N$, and $c = (-1,0)$. Define
$$W_R = \overline{ab_1} \cup \bigcup \{\overline{a_nb_n}: n \in \mathbb N\}
\quad \text{and} \quad W = \overline{ca} \cup W_R.$$

The dendrites $W_R$ and $W$ are called the
\es{comb $W_R$}{comb WR}
 and the
\es{comb $W$}{comb W}
, or (generally)
\es{locally connected combs}{locally connected comb}
.

See Figures A--B.

\FIGURE{A}{comb $W_R$}

\FIGURE{B}{comb $W$}
%Figure as in \cite[Fig. 1, p. 2]{Arevalo+2001a} (for $W$).

The dendrites $F_\omega$, $W_R$ and $W$ are exploited in the
following characterizations.
\rostere
\item A dendrite is a tree if and only if it contains neither a copy of
$F_\omega$ nor of $W_R$, \cite[Theorem 3.1, p. 3]{Arevalo+2001a}.
\item\label{ex-lccombs-clends} A dendrite has the set of all
its end points closed if
and only if it contains neither a copy of $F_\omega$ nor of $W$,
\cite[Corollary 5.4, p. 11]{Arevalo+2001a}.
\rosteree
