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The next two
examples are defined in [Arévalo et al. 2001, p. 3]. Let
stand for the straight line segment from
to in the plane. In the plane, let
for each
, and
. Define
and
The dendrites and are called the
comb
and the
comb
, or (generally)
locally connected combs
.
See Figures AB.
Figure 1.3.4:
( A ) comb

Figure 1.3.4:
( B ) comb

The dendrites , and are exploited in the
following characterizations.
 A dendrite is a tree if and only if it contains neither a copy of
nor of , [Arévalo et al. 2001, Theorem 3.1, p. 3].
 A dendrite has the set of all
its end points closed if
and only if it contains neither a copy of nor of ,
[Arévalo et al. 2001, Corollary 5.4, p. 11].
Here you can find source files
of this example.
Here you can check the table
of properties of individual continua.
Here you can read Notes
or
write to Notes
ies of individual continua.
Next: Universal dendrites
Up: Dendrites
Previous: The locally connected fan
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
20011130