Universal Dendrite D₃

The Universal Dendrite D₃ is obtained by the same procedure as the Waewski's 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 {T_n} and the Universal Dendrite $\mathbb{D}_3$ is the closure of their union. The Universal Dendrite ${\bf D_3}$ is homogeneous with respect to the monotone mappings. For details see [38, p.362].

Figure ( A ) Universal Dendrite D₃


Figure ( B ) Universal Dendrite D₃


Source files: a.eps . a.gif . b.gif . example.htm . figure.mws . latex.tex . title.txt .

Here you can read Notes or write to Notes.