Omiljanowski dendrite

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The Omiljanowski dendrite, usually denoted $L_0$, is the following dendrite:
Omiljanowski dendrite.gif

Properties

Theorem: All ramification points of $L_0$ are of order 3.

Proof:

Theorem: The set $R(L_0)$ of all ramification points of $L_0$ is discrete (hence nowhere dense).

Proof:

Theorem: For each maximal arc $A$ in $L_0$ the closure of the set $A \cap R(L_0)$ contains a homeomorphic copy of the Cantor set.

Proof:

Theorem: $L_0$ is monotonically equivalent to the dendrite $D_3$.

Proof: