{Self-homeomorphic dendrites}

Below we present some examples of dendrites that illustrate relations
between variants of self-homeomorphic properties.
\rostere
\item There is a \g{strongly
pointwise self-homeomorphic} dendrite which is not of the
form \gs{$D_S$}{dendrite DS} for some $S \subset \{3, 4,
\dots, \omega\}$, see \cite[Example 6.11, p. 232, and Fig.
4, p. 233]{CharatonikW+1994a}. Note that, according to
Property~\ref{ex-other-universal-dendrites-spsh}
in~\ref{ex-other-universal-dendrites}
each dendrite $D_S$ is strongly pointwise self-homeomorphic.
This example shows that the opposite implication does not
hold. Some additional properties of the example are shown in
\cite[Example 2.1, p. 152]{Pyrih1999b}.
See Figure A.

\FIGURE{A}{an example of self-homeomorphic dendrite}


\item There is a \g{strongly
self-homeomorphic} and \g{pointwise self-homeomorphic} dendrite
which is not \g{strongly
pointwise self-homeomorphic}, see \cite[Example 6.12, p.
233]{CharatonikW+1994a}.

\item There is a strongly self-homeomorphic dendrite which is not pointwise
self-homeomorphic, see \cite[Example 2.1, p. 572]{Pyrih1999a}.
Dendrites having this property are studied in \cite{Charatonik+XXXXc}.

See Figure B.

\FIGURE{B}{an example of strongly self-homeomorphic
dendrite}

\rosteree
