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The
Universal Dendrite
is obtained by the same procedure as the
Wazewski Universal Dendrite just instead of locally
connected fans we use simple triods.
We start with a simple triod T. Denote T1=T. Now we
attach sufficiently small copies of T (with one
end point as the attaching point) to all midpoints of all
maximal free arcs in T1 and obtain a dendrite
T2. Continuing in this fashion, we obtain the sequence of
dendrites {Tn} and the Universal Dendrite
is the closure of their union.
The Universal Dendrite
is homogeneous with
respect to the monotone mappings. For details see
[38, p.362].
Universal Dendrite ${\bf D_3}$- fig.
a
Universal Dendrite ${\bf D_3}$- fig.
b
Source files:
a.eps .
a.gif .
b.gif .
example.htm .
figure.mws .
latex.tex .
title.txt .
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Janusz J. Charatonik and Pavel Pyrih
2000-09-21