{The locally connected fan}
\label{ex-Fomega}

Another simple example is the
\e{locally connected fan}
$F_\omega$. It is defined as the union of countably many
straight line segments of length tending to $0$, emanating
from a point $p$ and disjoint out of $p$. Thus $F_\omega$ is
the dendrite with only one ramification point whose order is
$\omega$.

\FIGURE{A}{locally connected fan $F_\omega$}
%Figure as in \cite[Fig. 1, p. 9]{Charatonik+1990a}

The following mapping properties of $F_\omega$ are known.

\rostere
\item\label{ex-Fomega-univ} $F_\omega$ is
\gs{universal}{universal space} in the
class of all $n$-ods for $n \in \mathbb N$.
\item Each \gs{open image}{open mapping} of $F_\omega$ is homeomorphic to
$F_\omega$, \cite[Proposition 9.4, p. 42]{Charatonik+1990a}.
\item A \g{confluent mapping} defined on $F_\omega$ is
open if and only if it is \gs{light}{light mapping},
\cite[Theorem 9.6, p. 42]{Charatonik+1990a}.
\rosteree
